Marston Morse and his mathematical works
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- Bull. Amer. Math. Soc. 3 (1980), 907-950
References
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1. Marston Morse, Proof of a general theorem on the linear dependence of P analytic functions of a single variable, Bull. Amer. Math. Soc. 23 (1916), 114-117.
- Harold Marston Morse, A One-to-One Representation of Geodesics on a Surface of Negative Curvature, Amer. J. Math. 43 (1921), no. 1, 33–51. MR 1506428, DOI 10.2307/2370306
- Harold Marston Morse, Recurrent geodesics on a surface of negative curvature, Trans. Amer. Math. Soc. 22 (1921), no. 1, 84–100. MR 1501161, DOI 10.1090/S0002-9947-1921-1501161-8
- Harold Marston Morse, A fundamental class of geodesics on any closed surface of genus greater than one, Trans. Amer. Math. Soc. 26 (1924), no. 1, 25–60. MR 1501263, DOI 10.1090/S0002-9947-1924-1501263-9
- Marston Morse, Relations between the critical points of a real function of $n$ independent variables, Trans. Amer. Math. Soc. 27 (1925), no. 3, 345–396. MR 1501318, DOI 10.1090/S0002-9947-1925-1501318-X 6. Marston Morse, The analysis and analysis situs of regular n-spreads in (n + s)-space, Proc. Nat. Acad. Sci. 13 (1927), 813-817.
- Marston Morse, The foundations of a theory in the calculus of variations in the large, Trans. Amer. Math. Soc. 30 (1928), no. 2, 213–274. MR 1501428, DOI 10.1090/S0002-9947-1928-1501428-X
- Marston Morse, Singular Points of Vector Fields Under General Boundary Conditions, Amer. J. Math. 51 (1929), no. 2, 165–178. MR 1506710, DOI 10.2307/2370703 9. Marston Morse, The critical points of functions and the calculus of variations in the large, Bull. Amer. Math. Soc. 35 (1929), 38-54.
- Marston Morse, The foundations of the calculus of variations in the large in $m$-space. I, Trans. Amer. Math. Soc. 31 (1929), no. 3, 379–404. MR 1501489, DOI 10.1090/S0002-9947-1929-1501489-9 11. Marston Morse, Closed extremals, Proc. Nat. Acad. Sci. 15 (1929), 856-959. 12. Marston Morse, The problems of Lagrange and Mayer under general end conditions, Proc. Nat. Acad. Sci. 16 (1930), 229-233.
- Marston Morse, A generalization of the sturm separation and comparison theorems in $n$-space, Math. Ann. 103 (1930), no. 1, 52–69. MR 1512617, DOI 10.1007/BF01455690 14. Marston Morse, The critical points of a function of n variables, Proc. Nat. Acad. Sci. 16 (1930), 777-779.
- Marston Morse, The critical points of a function of $n$ variables, Trans. Amer. Math. Soc. 33 (1931), no. 1, 72–91. MR 1501576, DOI 10.1090/S0002-9947-1931-1501576-4 16. Marston Morse, The order of vanishing of the determinant of a conjugate base, Proc. Nat. Acad. Sci. 17 (1931), 319-320. 17. Marston Morse, The problems of Lagrange and Mayer with variable endpoints, by M. Morse and Sumner Byron Myers, Proc. Amer. Acad. Arts and Sci. 66 (1931), 235-253.
- Marston Morse, Closed extremals, Ann. of Math. (2) 32 (1931), no. 3, 549–566. MR 1503016, DOI 10.2307/1968251
- Marston Morse, Sufficient conditions in the problem of Lagrange with fixed end points, Ann. of Math. (2) 32 (1931), no. 3, 567–577. MR 1503017, DOI 10.2307/1968252
- Marston Morse, Sufficient Conditions in the Problem of Lagrange with Variable End Conditions, Amer. J. Math. 53 (1931), no. 3, 517–546. MR 1507924, DOI 10.2307/2371163
- Marston Morse, The foundations of a theory of the calculus of variations in the large in $m$-space. II, Trans. Amer. Math. Soc. 32 (1930), no. 4, 599–631. MR 1501555, DOI 10.1090/S0002-9947-1930-1501555-6 22. Marston Morse, A characterization of fields in the calculus of variations, by M. Morse and S. B. Littauer, Proc. Nat. Acad. Sci. 18 (1932), 724-730. 23. Marston Morse, The calculus of variations in the large, Verhandlungen des Internationalen Mathematiker-Kongresses Zürich, 1932, Vol. 1, pp. 173-188. 24. Marston Morse, Does instability imply transitivity?, Proc. Nat. Acad. Sci. 20 (1934), 46-50. 25. Marston Morse, On certain invariants of closed extremals, by M. Morse and Everett Pitcher, Proc. Nat Acad. Sci. 20 (1934), 282-287.
- Marston Morse and George Booth Van Schaack, The critical point theory under general boundary conditions, Ann. of Math. (2) 35 (1934), no. 3, 545–571. MR 1503179, DOI 10.2307/1968750
- Marston Morse, Sufficient conditions in the problem of Lagrange without assumptions of normalcy, Trans. Amer. Math. Soc. 37 (1935), no. 1, 147–160. MR 1501780, DOI 10.1090/S0002-9947-1935-1501780-9 28. Marston Morse, Instability and transitivity, Jour. de Mathématiques, Paris 14 (1935), 49-71. 29. Marston Morse, Abstract critical sets, by M. Morse and George B. Van Schaack, Proc. Nat. Acad. Sci. 21 (1935), 258-263. 30. Marston Morse, Generalized concavity theorems, Proc. Nat. Acad. Sci. 21 (1935), 359-362. 31. Marston Morse, Three theorems on the envelope of extremals, Proc. Nat. Acad. Sci. 21 (1935), 619-621; Bull. Amer. Math. Soc. 42 (1936), 136-144. 32. Marston Morse, Functional topology and abstract variational theory, Proc. Nat. Acad. Sci. 22 (1936), 313-319.
- Marston Morse and George B. Van Schaack, Critical point theory under general boundary conditions, Duke Math. J. 2 (1936), no. 2, 220–242. MR 1545920, DOI 10.1215/S0012-7094-36-00220-X
- Marston Morse and Walter Leighton, Singular quadratic functionals, Trans. Amer. Math. Soc. 40 (1936), no. 2, 252–286. MR 1501873, DOI 10.1090/S0002-9947-1936-1501873-7 35. Marston Morse, A special parametrization of curves, Bull. Amer. Math. Soc. 42 (1936), 915-922.
- Marston Morse, Functional topology and abstract variational theory, Ann. of Math. (2) 38 (1937), no. 2, 386–449. MR 1503341, DOI 10.2307/1968559
- Marston Morse, The index theorem in the calculus of variations, Duke Math. J. 4 (1938), no. 1, 231–246. MR 1546047, DOI 10.1215/S0012-7094-38-00418-1 38. Marston Morse, Functional topology and abstract variational theory, Proc. Nat. Acad. Sci. 24 (1938), 326-330.
- Marston Morse and Gustav A. Hedlund, Symbolic Dynamics, Amer. J. Math. 60 (1938), no. 4, 815–866. MR 1507944, DOI 10.2307/2371264
- Marston Morse and C. Tompkins, The existence of minimal surfaces of general critical types, Ann. of Math. (2) 40 (1939), no. 2, 443–472. MR 1503471, DOI 10.2307/1968932
- Marston Morse, Sur le calcul des variations, Ann. Inst. H. Poincaré 9 (1939), 1–11 (French). MR 460 42. Marston Morse, La dynamique symbolique, Bull. Soc. Math. France 67 (1939), 1-7. 43. Marston Morse, Symbolic dynamics. II. Sturmian sequences, by M. Morse and G. A. Hedlund, Amer. J. Math. 61 (1940), 1-42.
- Marston Morse, Rank and span in functional topology, Ann. of Math. (2) 41 (1940), 419–454. MR 1927, DOI 10.2307/1969014
- Marston Morse, The first variation in minimal surface theory, Duke Math. J. 6 (1940), 263–289. MR 2476 46. Marston Morse, Twentieth century mathematics, Amer. Scholar 9 (1940), 499-504.
- Marston Morse and C. B. Tompkins, Unstable minimal surfaces of higher topological types, Proc. Nat. Acad. Sci. U.S.A. 26 (1940), 713–716. MR 3481, DOI 10.1073/pnas.26.12.713
- Marston Morse, A mathematical theory of equilibrium with applications to minimal surface theory, Science 93 (1941), 69–71. MR 6028, DOI 10.1126/science.93.2404.69
- Marston Morse and C. Tompkins, Minimal surfaces not of minimum type by a new mode of approximation, Ann. of Math. (2) 42 (1941), 62–72. MR 3482, DOI 10.2307/1968987
- Marston Morse and C. Tompkins, Corrections to our paper on the existence of minimal surfaces of general critical types, Ann. of Math. (2) 42 (1941), 331. MR 3483, DOI 10.2307/1969002 51. Marston Morse, Mathematics in the defense program, by M. Morse and W. L. Hart, The Math. Teacher, May 1941, pp. 195-202.
- Marston Morse and C. Tompkins, Unstable minimal surfaces of higher topological structure, Duke Math. J. 8 (1941), 350–375. MR 4744
- Marston Morse and C. Tompkins, The continuity of the area of harmonic surfaces as a function of the boundary representations, Amer. J. Math. 63 (1941), 825–838. MR 6027, DOI 10.2307/2371624 54. Marston Morse, Report on the War Preparedness Committee of the AMS and MAA at the Chicago meeting, Bull. Amer. Math. Soc. 47 (1941), 829-831.
- Marston Morse, What is analysis in the large?, Amer. Math. Monthly 49 (1942), 358–364. MR 6351, DOI 10.2307/2303130
- Marston Morse and Gustav A. Hedlund, Manifolds without conjugate points, Trans. Amer. Math. Soc. 51 (1942), 362–386. MR 6479, DOI 10.1090/S0002-9947-1942-0006479-X
- Marston Morse, Lacunary type number sequences in global analysis, J. Math. Pures Appl. (9) 57 (1978), no. 1, 87–98. MR 497124
- George Ewing and Marston Morse, The variational theory in the large including the non-regular case. I, Ann. of Math. (2) 44 (1943), 339–353. MR 10250, DOI 10.2307/1968967
- Marston Morse, Functional topology, Bull. Amer. Math. Soc. 49 (1943), 144–149. MR 9102, DOI 10.1090/S0002-9904-1943-07879-2
- Marston Morse and Gustav A. Hedlund, Unending chess, symbolic dynamics and a problem in semigroups, Duke Math. J. 11 (1944), 1–7. MR 9788
- Marston Morse and Maurice Heins, Topological methods in the theory of functions of a single complex variable. I. Deformation types of locally simple plane curves, Ann. of Math. (2) 46 (1945), 600–624. MR 16466, DOI 10.2307/1969200
- Marston Morse, The topology of pseudo-harmonic functions, Duke Math. J. 13 (1946), 21–42. MR 15626
- Marston Morse, George David Birkhoff and his mathematical work, Bull. Amer. Math. Soc. 52 (1946), 357–391. MR 16341, DOI 10.1090/S0002-9904-1946-08553-5
- Marston Morse and Maurice Heins, Topological methods in the theory of functions of a complex variable, Bull. Amer. Math. Soc. 53 (1947), 1–14. MR 20129, DOI 10.1090/S0002-9904-1947-08727-9
- Marston Morse and Maurice Heins, Deformation classes of meromorphic functions and their extensions to interior transformations, Acta Math. 79 (1947), 51–103. MR 20128, DOI 10.1007/BF02404694
- Marston Morse, Functions on a metric space and a setting for isoperimetric problems, Studies and Essays Presented to R. Courant on his 60th Birthday, January 8, 1948, Interscience Publishers, Inc., New York, 1948, pp. 253–263. MR 0022659
- Marston Morse, A positive, lower semi-continuous, non-degenerate function on a metric space, Fund. Math. 35 (1948), 47–78. MR 28023, DOI 10.4064/fm-35-1-47-78
- Marston Morse, $L$-$S$- homotopy classes of locally simple curves, Ann. Soc. Polon. Math. 21 (1948), 236–256 (1949). MR 0031237
- Marston Morse, Equilibria in nature—stable and unstable, Proc. Amer. Philos. Soc. 93 (1949), 222–225. MR 29351
- Marston Morse and William Transue, The Fréchet variation and the convergence of multiple Fourier series, Proc. Nat. Acad. Sci. U.S.A. 35 (1949), 395–399. MR 30587, DOI 10.1073/pnas.35.7.395
- Marston Morse and William Transue, Integral representations of bilinear functionals, Proc. Nat. Acad. Sci. U.S.A. 35 (1949), 136–143. MR 29478, DOI 10.1073/pnas.35.3.136
- Marston Morse and William Transue, Functionals of bounded Fréchet variation, Canad. J. Math. 1 (1949), 153–165. MR 29425, DOI 10.4153/cjm-1949-014-0 73. Marston Morse, Functionals F bilinear over the product A x B of two p-normed vector spaces: I. The representation of F, by M. Morse and W. Transue, Ann. of Math. (2) 50 (1949), 777-815; II. Admissible spaces A, Ann. of Math. (2) 51 (1950), 576-614. 74. Marston Morse, Les progrès de l’analyse variationnelle globale et son programme, Rendiconti di Matematica e delle sue applicazioni, Serie V, 70 (3) (4) (1948), 1-11.
- Marston Morse, Topological methods in the theory of functions of a complex variable, Ann. Mat. Pura Appl. (4) 28 (1949), 21–24. MR 35337, DOI 10.1007/BF02411117
- Marston Morse and William Transue, A characterization of the bilinear sums associated with the classical second variation, Ann. Mat. Pura Appl. (4) 28 (1949), 25–68. MR 38579, DOI 10.1007/BF02411118
- Marston Morse, $L$-$S$-homotopy classes on the topological image of a projective plane, Bull. Amer. Math. Soc. 55 (1949), 981–1003. MR 33006, DOI 10.1090/S0002-9904-1949-09326-6
- Marston Morse and William Transue, The Fréchet variation and a generalization for multiple Fourier series of the Jordan test, Riv. Mat. Univ. Parma 1 (1950), 3–18. MR 33907
- Marston Morse and William Transue, The Fréchet variation, sector limits, and left decompositions, Canad. J. Math. 2 (1950), 344–374. MR 37340, DOI 10.4153/cjm-1950-033-1
- Marston Morse and William Transue, A calculus for Fréchet variations, J. Indian Math. Soc. (N.S.) 14 (1950), 65–117. MR 39043
- Marston Morse, Bowls of a non-degenerate function on a compact differentiable manifold, Differential and Combinatorial Topology (A Symposium in Honor of Marston Morse), Princeton Univ. Press, Princeton, N.J., 1965, pp. 81–103. MR 0182026
- Marston Morse and William Transue, Norms of distribution functions associated with bilinear functionals, Contributions to Fourier Analysis, Annals of Mathematics Studies, no. 25, Princeton University Press, Princeton, N.J., 1950, pp. 104–144. MR 0036940
- Marston Morse, Bilinear functionals over $C\times C$, Acta Sci. Math. (Szeged) 12 (1950), 41–48. MR 34528
- Marston Morse, Recent advances in variational theory in the large, Proceedings of the International Congress of Mathematicians, Cambridge, Mass., 1950, vol. 2, Amer. Math. Soc., Providence, R.I., 1952, pp. 143–156. MR 0044758
- Marston Morse and William Transue, A new implication of the Young-Pollard convergence criteria for a Fourier Series, Duke Math. J. 18 (1951), 563–571. MR 47171
- Marston Morse, Trends in analysis, J. Franklin Inst. 251 (1951), 33–43. MR 38288, DOI 10.1016/0016-0032(51)90893-9 87. Marston Morse, Mathematics and the arts, Yale Review 40 (1951), 604-612. 75th birthday of Robert Frost Essay given at Kenyon College.
- Marston Morse, Homology relations on regular orientable manifolds, Proc. Nat. Acad. Sci. U.S.A. 38 (1952), 247–258. MR 48031, DOI 10.1073/pnas.38.3.247
- James A. Jenkins and Marston Morse, Contour equivalent pseudoharmonic functions and pseudoconjugates, Amer. J. Math. 74 (1952), 23–51. MR 48642, DOI 10.2307/2372067
- Marston Morse and Emilio Baiada, Homotopy and homology related to the Schoenflies problem, Ann. of Math. (2) 58 (1953), 142–165. MR 56922, DOI 10.2307/1969825
- James A. Jenkins and Marston Morse, Topological methods on Riemann surfaces. Pseudoharmonic functions, Contributions to the theory of Riemann surfaces, Annals of Mathematics Studies, no. 30, Princeton University Press, Princeton, N.J., 1953, pp. 111–139. MR 0057339
- M. Morse, The existence of pseudoconjugates on Riemann surfaces, Fund. Math. 39 (1952), 269–287 (1953). MR 57338, DOI 10.4064/fm-39-1-269-287 93. Marston Morse, The generalized Fréchet variation and Riesz-Young-Hausdorff type theorems, by M. Morse with W. Transue, Rend. Circ. Math. Palermo, Serie II, Tome II (1953), 35 pp.
- James Jenkins and Marston Morse, Conjugate nets, conformal structure, and interior transformations on open Riemann surfaces, Proc. Nat. Acad. Sci. U.S.A. 39 (1953), 1261–1268. MR 58724, DOI 10.1073/pnas.39.12.1261 95. Marston Morse, Conjugate nets on an open Riemann surface, by M. Morse with J. Jenkins, Proc. Univ. Michigan Conf., June 1953.
- James Jenkins and Marston Morse, Curve families $F^*$ locally the level curves of a pseudoharmonic function, Acta Math. 91 (1954), 1–42. MR 62292, DOI 10.1007/BF02393423
- Marston Morse and William Transue, Semi-normed vector spaces with duals of integral type, J. Analyse Math. 4 (1954/55), 149–186. MR 73677, DOI 10.1007/BF02787719
- Marston Morse, Bimeasures and their integral extensions, Ann. Mat. Pura Appl. (4) 39 (1955), 345–356. MR 75273, DOI 10.1007/BF02410778
- Marston Morse and William Transue, $C$-bimeasures $\Lambda$ and their superior integrals $\Lambda ^*$, Rend. Circ. Mat. Palermo (2) 4 (1955), 270–300 (1956). MR 86115, DOI 10.1007/BF02854200
- Marston Morse and William Transue, The representation of a C-bimeasure on a general rectangle, Proc. Nat. Acad. Sci. U.S.A. 42 (1956), 89–95. MR 75274, DOI 10.1073/pnas.42.2.89
- Marston Morse, La construction topologique d’un réseau isotherme sur une surface ouverte, J. Math. Pures Appl. (9) 35 (1956), 67–75 (French). MR 77648
- Marston Morse and William Transue, $C$-bimeasures $\Lambda$ and their integral extensions, Ann. of Math. (2) 64 (1956), 480–504. MR 86116, DOI 10.2307/1969597
- Marston Morse and William Transue, Products of a $C$-measure and a locally integrable mapping, Canadian J. Math. 9 (1957), 475–486. MR 91982, DOI 10.4153/CJM-1957-056-4
- Marston Morse, Differentiable mappings in the Schoenflies problem, Proc. Nat. Acad. Sci. U.S.A. 44 (1958), 1068–1072. MR 110108, DOI 10.1073/pnas.44.10.1068
- Marston Morse and William Transue, Vector subspaces $A$ of $C^{E}$ with duals of integral type, J. Math. Pures Appl. (9) 37 (1958), 343–363. MR 99583
- M. Morse and W. Transue, The existence of vector function spaces with duals of integral type, Colloq. Math. 6 (1958), 95–117. MR 101998, DOI 10.4064/cm-6-1-95-117
- Marston Morse and William Transue, The local characterization of vector function spaces with duals of integral type, J. Analyse Math. 6 (1958), 225–260. MR 101997, DOI 10.1007/BF02790237
- $\{$Memorial issue for Marston Morse$\}$, Academia Sinica, Institute of Mathematics, Taipei, 1978. Bull. Inst. Math. Acad. Sinica 6 (1978), no. 2, part 1. MR 0497417 109. Marston Morse, Mathematics, the arts and freedom, Thought (Fordham Univ. Quarterly) 34 (1959), 16-24.
- Marston Morse, Differentiable mappings in the Schoenflies problem, Proc. Nat. Acad. Sci. U.S.A. 44 (1958), 1068–1072. MR 110108, DOI 10.1073/pnas.44.10.1068
- Marston Morse, Topologically non-degenerate functions on a compact $n$-manifold $M$, J. Analyse Math. 7 (1959), 189–208. MR 113233, DOI 10.1007/BF02787685
- Marston Morse, Fields of geodesics issuing from a point, Proc. Nat. Acad. Sci. U.S.A. 46 (1960), 105–111. MR 113231, DOI 10.1073/pnas.46.1.105
- Marston Morse, The existence of polar non-degenerate functions on differentiable manifolds, Ann. of Math. (2) 71 (1960), 352–383. MR 113232, DOI 10.2307/1970086
- Marston Morse, A reduction of the Schoenflies extension problem, Bull. Amer. Math. Soc. 66 (1960), 113–115. MR 117694, DOI 10.1090/S0002-9904-1960-10420-X
- Marston Morse, The existence of non-degenerate functions on a compact differentiable $m$-manifold $M$, Ann. Mat. Pura Appl. (4) 49 (1960), 117–128. MR 120650, DOI 10.1007/BF02414043
- Harold Marston Morse, Recurrent geodesics on a surface of negative curvature, Trans. Amer. Math. Soc. 22 (1921), no. 1, 84–100. MR 1501161, DOI 10.1090/S0002-9947-1921-1501161-8
- William Huebsch and Marston Morse, An explicity solution of the Schoenflies extension problem, J. Math. Soc. Japan 12 (1960), 271–289. MR 206928, DOI 10.2969/jmsj/01230271
- William Huebsch and Marston Morse, A singularity in the Schoenflies extension, Proc. Nat. Acad. Sci. U.S.A. 46 (1960), 1100–1102. MR 119213, DOI 10.1073/pnas.46.8.1100
- Marston Morse, On elevating manifold differentiability, J. Indian Math. Soc. (N.S.) 24 (1960), 379–400 (1961). MR 141135
- William Huebsch and Marston Morse, The dependence of the Schoenflies extension on an accessory parameter, J. Analyse Math. 8 (1960/61), 209–271. MR 145547, DOI 10.1007/BF02786851 121. Marston Morse, (With W. Huebsch) Abstracts: A characterization of an analytic n-ball, and A. Schoenflies extension of a real analytic diffeomorphism of S into W. (Multilithed April 17, 1961.)
- Marston Morse, Boundary values of partial derivatives of Poisson integral, An. Acad. Brasil. Ci. 33 (1961), 131–139. MR 164052
- William Huebsch and Marston Morse, Conical singular points of diffeomorphisms, Bull. Amer. Math. Soc. 67 (1961), 490–493. MR 145548, DOI 10.1090/S0002-9904-1961-10651-4
- William Huebsch and Marston Morse, Schoenflies extensions of analytic families of diffeomorphisms, Math. Ann. 144 (1961), 162–174. MR 133835, DOI 10.1007/BF01451335
- William Huebsch and Marston Morse, The Schoenflies extension in the analytic case, Ann. Mat. Pura Appl. (4) 54 (1961), 359–378. MR 144353, DOI 10.1007/BF02415363
- M. Morse, Schoenflies problems, Fund. Math. 50 (1961/62), 319–332. MR 148082, DOI 10.4064/fm-50-3-319-332
- William Huebsch and Marston Morse, Schoenflies extensions without interior differential singularities, Ann. of Math. (2) 76 (1962), 18–54. MR 146847, DOI 10.2307/1970263
- Marston Morse, Topological, differential, and analytic formulations of Schoenflies problems, Rend. Mat. e Appl. (5) 21 (1962), 286–295. MR 154295 129. Marston Morse, (With W. Huebsch) Analytic diffeomorphisms approximating C, Rend. Circ. Mat. Palermo 11 (1962), 1-22.
- William Huebsch and Marston Morse, Diffeomorphisms of manifolds, Rend. Circ. Mat. Palermo (2) 11 (1962), 291–318. MR 172297, DOI 10.1007/BF02843877
- Marston Morse, Schoenflies extensions and differentiable isotopies, J. Math. Pures Appl. (9) 42 (1963), 29–41. MR 149497
- Marston Morse, An arbitrarily small analytic mapping into $R_{+}$ of a proper, regular, analytic $r$-manifold in $E_{m}$, Ist. Lombardo Accad. Sci. Lett. Rend. A 97 (1963), 650–660 (English, with Italian summary). MR 177364
- Marston Morse, Harmonic extensions, Monatsh. Math. 67 (1963), 317–325. MR 158088, DOI 10.1007/BF01299582
- William Huebsch and Marston Morse, The dependence of the Schoenflies extension on an accessory parameter (the topological case), Proc. Nat. Acad. Sci. U.S.A. 50 (1963), 1036–1037. MR 182957, DOI 10.1073/pnas.50.6.1036
- William Huebsch and Marston Morse, The bowl theorem and a model nondegenerate function, Proc. Nat. Acad. Sci. U.S.A. 51 (1964), 49–51. MR 160245, DOI 10.1073/pnas.51.1.49
- William Huebsch and Marston Morse, Conditioned differentiable isotopies, Differential Analysis, Bombay Colloq., 1964, Oxford Univ. Press, London, 1964, pp. 1–25. MR 0185603
- Marston Morse, The elimination of critical points of a non-degenerate function on a differentiable manifold, J. Analyse Math. 13 (1964), 257–316. MR 184256, DOI 10.1007/BF02786621
- Marston Morse, Bowls, $f$-fibre-bundles and the alteration of critical values, An. Acad. Brasil. Ci. 36 (1964), 245–259. MR 178478
- Marston Morse, Bowls of a non-degenerate function on a compact differentiable manifold, Differential and Combinatorial Topology (A Symposium in Honor of Marston Morse), Princeton Univ. Press, Princeton, N.J., 1965, pp. 81–103. MR 0182026
- Marston Morse, Quadratic forms $\Theta$ and $\Theta$-fibre-bundles, Ann. of Math. (2) 81 (1965), 303–340. MR 173272, DOI 10.2307/1970618
- W. Huebsch and Marston Morse, A model non-degenerate function, Rev. Roumaine Math. Pures Appl. 10 (1965), 691–722. MR 206985
- Marston Morse, The reduction of a function near a nondegenerate critical point, Proc. Nat. Acad. Sci. U.S.A. 54 (1965), 1759–1763. MR 189056, DOI 10.1073/pnas.54.6.1759 143. Marston Morse, Projective methods (in photogrammetry), Photogrammetric Engineering, Sept. 1966, pp. 849-855. 144. Marston Morse, (With J. Cantwell) Diffeomorphism including automorphisms of π1(T), Topology 4 (1966), 323-341.
- Marston Morse, Non-degenerate functions on abstract diffentiable manifolds $M_{n}$, J. Analyse Math. 19 (1967), 231–272. MR 216515, DOI 10.1007/BF02788720
- Marston Morse, Nondegenerate real-valued differentiable functions, Proc. Nat. Acad. Sci. U.S.A. 57 (1967), 32–38. MR 206976, DOI 10.1073/pnas.57.1.32 147. Marston Morse, Focal sets of regular manifolds M, J. Differential Geometry 1 (1967), 1-19.
- Marston Morse, Bowls, $f$-fiber bundles, and the alteration of critical values, Proc. Nat. Acad. Sci. U.S.A. 60 (1968), 1156–1159. MR 231408, DOI 10.1073/pnas.60.4.1156
- Marston Morse and Stewart Scott Cairns, Singular homology over $Z$ on topological manifolds, J. Differential Geometry 3 (1969), 257–288. MR 270375
- Marston Morse and Stewart S. Cairns, A setting for a theorem of Bott, Proc. Nat. Acad. Sci. U.S.A. 65 (1970), 8–9. MR 253372, DOI 10.1073/pnas.65.1.8 151. Marston Morse, Mathematics in our culture, The Spirit and the Uses of the Mathematical Sciences by T. L. Saaty and F. J. Weyl, McGraw-Hill, New York, 1969, pp. 105-120.
- Marston Morse, Equilibrium points of harmonic potentials, J. Analyse Math. 23 (1970), 281–296. MR 277737, DOI 10.1007/BF02795505
- Marston Morse and Stewart Scott Cairns, Elementary quotients of abelian groups, and singular homology on manifolds, Nagoya Math. J. 39 (1970), 167–198. MR 265457, DOI 10.1017/S0027763000013787
- Marston Morse, Subordinate quadratic forms and their complementary forms, Proc. Nat. Acad. Sci. U.S.A. 68 (1971), 579. MR 287558, DOI 10.1073/pnas.68.3.579
- Marston Morse, Model families of quadratic forms, Proc. Nat. Acad. Sci. U.S.A. 68 (1971), 914–915. MR 284457, DOI 10.1073/pnas.68.5.914
- Marston Morse and Stewart S. Cairns, Orientation of differentiable manifolds, J. Differential Geometry 6 (1971/72), 1–31. MR 331415
- Marston Morse, Subordinate quadratic forms and their complementary forms, Rev. Roumaine Math. Pures Appl. 16 (1971), 559–569. MR 308050
- Marston Morse and Stewart S. Cairns, Singular homology on an untriangulated manifold, J. Differential Geometry 7 (1972), 1–17. MR 368016
- Marston Morse, Axial presentations of regular arcs on $M_{n}$, Proc. Nat. Acad. Sci. U.S.A. 69 (1972), 3504–3505. MR 321118, DOI 10.1073/pnas.69.12.3504
- Marston Morse, Singular quadratic functionals, Math. Ann. 201 (1973), 315–340. MR 343150, DOI 10.1007/BF01428198
- Marston Morse, $F$-deformations and $F$-tractions, Proc. Nat. Acad. Sci. U.S.A. 70 (1973), 1634–1635. MR 321098, DOI 10.1073/pnas.70.6.1634
- Marston Morse, Fréchet curve classes, J. Math. Pures Appl. (9) 53 (1974), 291–298. MR 365622
- Marston Morse, Singleton critical values, Bull. Inst. Math. Acad. Sinica 2 (1974), 317–333. MR 356092
- Dale Landis and Marston Morse, Geodesic joins and Fréchet curve classes, Rend. Mat. (6) 8 (1975), 161–185 (English, with Italian summary). MR 397783
- Marston Morse, Connectivities $R_{i}$ of Fréchet spaces in variational topology, Proc. Nat. Acad. Sci. U.S.A. 72 (1975), 2069–2070. MR 440607, DOI 10.1073/pnas.72.6.2069
- Marston Morse, Topologically nondegenerate functions, Fund. Math. 88 (1975), no. 1, 17–52. MR 418128, DOI 10.4064/fm-88-1-17-52
- Dale Landis and Marston Morse, Tractions in critical point theory, Rocky Mountain J. Math. 5 (1975), 379–399. MR 383458, DOI 10.1216/RMJ-1975-5-3-379
- Marston Morse, Fréchet numbers in global variational analysis, Houston J. Math. 2 (1976), no. 3, 387–403. MR 420702
- Stewart S. Cairns and Marston Morse, Fréchet numbers and geodesics on surfaces, Bull. Inst. Math. Acad. Sinica 4 (1976), no. 1, 7–34. MR 407888
- Marston Morse, Conjugate points on a limiting extremal, Proc. Nat. Acad. Sci. U.S.A. 73 (1976), no. 6, 1800–1801. MR 405497, DOI 10.1073/pnas.73.6.1800
- Marston Morse, Extremal limits of nondegenerate extremals, Rend. Mat. (6) 9 (1976), no. 4, 621–632 (1977) (English, with Italian summary). MR 436208 172. Marston Morse, Tubular presentations π of subsets of manifolds, Proc. Nat. Acad. Sci. 74 (1977), 2209-2210.
- Marston Morse, Nondegenerate point pairs in global variational analysis, J. Differential Geometry 11 (1976), no. 4, 617–632. MR 455025
- Marston Morse, Uses of the Fréchet numbers $R_{i}(M_{n})$ of a smooth manifold, Houston J. Math. 3 (1977), no. 4, 503–513. MR 467811
- Marston Morse, Lacunary type number sequences in global analysis, J. Math. Pures Appl. (9) 57 (1978), no. 1, 87–98. MR 497124
- Marston Morse, The Fréchet numbers of the differentiable product of two compact, connected, smooth manifolds, Bull. Inst. Math. Acad. Sinica 6 (1978), no. 2, 215–246. Memorial issue for Marston Morse; Edited and completed by Stewart S. Cairns. MR 512338
- Marston Morse, The calculus of variations in the large, American Mathematical Society Colloquium Publications, vol. 18, American Mathematical Society, Providence, RI, 1996. Reprint of the 1932 original. MR 1451874, DOI 10.1090/coll/018 2. Marston Morse, Functional topology and abstract variational theory, Mémorial des Sciences Mathématiques 92, Gauthier-Villars, Paris, 1939.
- Marston Morse, Topological Methods in the Theory of Functions of a Complex Variable, Annals of Mathematics Studies, No. 15, Princeton University Press, Princeton, N. J., 1947. MR 0021089 4. Marston Morse, Symbolic dynamics, Lectures of 1938 with New Preface, 1966, 87 pp. (Notes by R. Oldenburger.) University Microfilms, 300 N. Zeeb Road, Ann Arbor, Mich. 48106.
- Marston Morse and Stewart S. Cairns, Critical point theory in global analysis and differential topology: An introduction, Pure and Applied Mathematics, Vol. 33, Academic Press, New York-London, 1969. MR 0245046
- Marston Morse, Variational analysis: critical extremals and Sturmian extensions, Pure and Applied Mathematics, Interscience Publishers [John Wiley & Sons], New York-London-Sydney, 1973. MR 0420368
- Marston Morse, Global variational analysis, Mathematical Notes, No. 16, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1976. Weierstrass integrals on a Riemannian manifold. MR 0494242
- Aldo Andreotti and Theodore Frankel, The Lefschetz theorem on hyperplane sections, Ann. of Math. (2) 69 (1959), 713–717. MR 177422, DOI 10.2307/1970034
- George D. Birkhoff, Dynamical systems with two degrees of freedom, Trans. Amer. Math. Soc. 18 (1917), no. 2, 199–300. MR 1501070, DOI 10.1090/S0002-9947-1917-1501070-3
- D. Birkoff, Quelques théorèmes sur le mouvement des systèmes dynamiques, Bull. Soc. Math. France 40 (1912), 305–323 (French). MR 1504693, DOI 10.24033/bsmf.909
- G. D. Birkhoff and M. R. Hestenes, Generalized minimax principle in the calculus of variations, Duke Math. J. 1 (1935), no. 4, 413–432. MR 1545886, DOI 10.1215/S0012-7094-35-00128-4
- Raoul Bott, Nondegenerate critical manifolds, Ann. of Math. (2) 60 (1954), 248–261. MR 64399, DOI 10.2307/1969631
- Raoul Bott, The stable homotopy of the classical groups, Ann. of Math. (2) 70 (1959), 313–337. MR 110104, DOI 10.2307/1970106
- Raoul Bott and Hans Samelson, Applications of the theory of Morse to symmetric spaces, Amer. J. Math. 80 (1958), 964–1029. MR 105694, DOI 10.2307/2372843
- Marston Morse, A reduction of the Schoenflies extension problem, Bull. Amer. Math. Soc. 66 (1960), 113–115. MR 117694, DOI 10.1090/S0002-9904-1960-10420-X
- René Deheuvels, Topologie d’une fonctionnelle, Ann. of Math. (2) 61 (1955), 13–72 (French). MR 69488, DOI 10.2307/1969619 [H1] J. Hadamard, Les surfaces à courbure opposées et leur lignes géodesiques, J. Math. Pures Appl. (5) 4 (1898).
- Gustav A. Hedlund, On the metrical transitivity of the geodesics on closed surfaces of constant negative curvature, Ann. of Math. (2) 35 (1934), no. 4, 787–808. MR 1503197, DOI 10.2307/1968495
- Wilhelm Klingenberg, Lectures on closed geodesics, Grundlehren der Mathematischen Wissenschaften, Vol. 230, Springer-Verlag, Berlin-New York, 1978. MR 0478069, DOI 10.1007/978-3-642-61881-9
- Barry Mazur, On embeddings of spheres, Bull. Amer. Math. Soc. 65 (1959), 59–65. MR 117693, DOI 10.1090/S0002-9904-1959-10274-3
- J. Milnor, Morse theory, Annals of Mathematics Studies, No. 51, Princeton University Press, Princeton, N.J., 1963. Based on lecture notes by M. Spivak and R. Wells. MR 0163331, DOI 10.1515/9781400881802
- P. S. Novikov, On periodic groups, Dokl. Akad. Nauk SSSR 127 (1959), 749–752 (Russian). MR 0106950
- Richard S. Palais, Morse theory on Hilbert manifolds, Topology 2 (1963), 299–340. MR 158410, DOI 10.1016/0040-9383(63)90013-2
- H. L. Royden, The analytic approximation of differentiable mappings, Math. Ann. 139 (1960), 171–179 (1960). MR 113229, DOI 10.1007/BF01352908 [S1] Seifert-Threlfall, Variationsrechnung im Grossen, Teubner, Leipzig, 1938.
- Stephen Smale, The generalized Poincaré conjecture in higher dimensions, Bull. Amer. Math. Soc. 66 (1960), 373–375. MR 124912, DOI 10.1090/S0002-9904-1960-10458-2
- S. Smale, A survey of some recent developments in differential topology, Bull. Amer. Math. Soc. 69 (1963), 131–145. MR 144351, DOI 10.1090/S0002-9904-1963-10901-5
- S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967), 747–817. MR 228014, DOI 10.1090/S0002-9904-1967-11798-1 [S5] G. Series, Symbolic dynamics for geodesic flows, Univ. Warwick, 1979.
- René Thom, Sur une partition en cellules associée à une fonction sur une variété, C. R. Acad. Sci. Paris 228 (1949), 973–975 (French). MR 29160, DOI 10.1073/pnas.21.11.619
Additional Information
- Journal: Bull. Amer. Math. Soc. 3 (1980), 907-950
- DOI: https://doi.org/10.1090/S0273-0979-1980-14824-7
- MathSciNet review: 585177