Morse inequalities for a dynamical system
Author:
Stephen Smale
Journal:
Bull. Amer. Math. Soc. 66 (1960), 43-49
DOI:
https://doi.org/10.1090/S0002-9904-1960-10386-2
MathSciNet review:
0117745
Full-text PDF Free Access
References | Additional Information
-
1. A. A. Andronov and L. S. Pontrjagin, Systèmes grossiers, Dokl. Akad. Nauk vol. 14 (1937) pp. 247-250.
- Earl A. Coddington and Norman Levinson, Theory of ordinary differential equations, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1955. MR 0069338
- H. F. DeBaggis, Dynamical systems with stable structures, Contributions to the Theory of Nonlinear Oscillations, vol. II, Princeton University Press, Princeton, 1952, pp. 37–59. MR 0051991
- L. È. Èl′sgol′c, An estimate for the number of singular points of a dynamical system defined on a manifold, Mat. Sbornik N.S. 26(68) (1950), 215–223 (Russian). MR 0034969
- R. K. Lashof and S. Smale, Self-intersections of immersed manifolds, J. Math. Mech. 8 (1959), 143–157. MR 0101522, DOI https://doi.org/10.1512/iumj.1959.8.58010
- Solomon Lefschetz, Differential equations: geometric theory, Pure and Applied Mathematics, Vol. VI, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1957. MR 0094488
- Daniel C. Lewis Jr., Invariant Manifolds Near an Invariant Point of Unstable Type, Amer. J. Math. 60 (1938), no. 3, 577–587. MR 1507339, DOI https://doi.org/10.2307/2371599
- 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
- M. M. Peixoto, On structural stability, Ann. of Math. (2) 69 (1959), 199–222. MR 101951, DOI https://doi.org/10.2307/1970100
- Everett Pitcher, Inequalities of critical point theory, Bull. Amer. Math. Soc. 64 (1958), 1–30. MR 96153, DOI https://doi.org/10.1090/S0002-9904-1958-10137-8
- Georges Reeb, Sur certaines propriétés topologiques des trajectoires des systèmes dynamiques, Acad. Roy. Belg. Cl. Sci. Mém. Coll. in 8$^\circ $ 27 (1952), no. 9, 64 (French). MR 58202 12. S. Smale, On structural stability, to appear.
- Shlomo Sternberg, Local contractions and a theorem of Poincaré, Amer. J. Math. 79 (1957), 809–824. MR 96853, DOI https://doi.org/10.2307/2372437
- 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
