Book Review
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1567363
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Book Information:
Author:
Robert Hermann
Title:
Cartanian geometry, nonlinear waves, and control theory
Additional book information:
Interdisciplinary Mathematics, volumes 20 and 21, Math. Sci. Press, Brookline, Mass., Part A, 1979, xv + 501 pp., $50.00; Part B, 1980, xii + 585 pp., $60.00.
Ralph Abraham and Jerrold E. Marsden, Foundations of mechanics, Benjamin/Cummings Publishing Co., Inc., Advanced Book Program, Reading, Mass., 1978. Second edition, revised and enlarged; With the assistance of Tudor Raţiu and Richard Cushman. MR 515141
V. Arnold, Les méthodes mathématiques de la mécanique classique, Éditions Mir, Moscow, 1976 (French). Traduit du russe par Djilali Embarek. MR 0474391
K. Bleuler and A. Reetz (eds.), Differential geometrical methods in mathematical physics, Lecture Notes in Mathematics, Vol. 570, Springer-Verlag, Berlin-New York, 1977. MR 0434688
Konrad Bleuler and Axel Reetz (eds.), Differential geometrical methods in mathematical physics. II, Lecture Notes in Mathematics, vol. 676, Springer, Berlin, 1978. MR 519605
Frederick Bloom, Modern differential geometric techniques in the theory of continuous distributions of dislocations, Lecture Notes in Mathematics, vol. 733, Springer, Berlin, 1979. MR 546839
6. R. W. Brockett, Finite dimensional linear systems, Wiley, New York, 1969.
R. W. Brockett, System theory on group manifolds and coset spaces, SIAM J. Control 10 (1972), 265–284. MR 0315559
R. W. Brockett, Lie theory and control systems defined on spheres, SIAM J. Appl. Math. 25 (1973), 213–225. MR 327337, DOI 10.1137/0125025
Roger W. Brockett, Nonlinear systems and differential geometry, Proc. IEEE 64 (1976), no. 1, 61–72. Recent trends in system theory. MR 0432255
Pavol Brunovský, A classification of linear controllable systems, Kybernetika (Prague) 6 (1970), 173–188 (English, with Czech summary). MR 284247
Christopher I. Byrnes (ed.), Partial differential equations and geometry, Lecture Notes in Pure and Applied Mathematics, vol. 48, Marcel Dekker, Inc., New York, 1979. MR 535586
Christopher I. Byrnes and Clyde F. Martin (eds.), Geometrical methods for the theory of linear systems, NATO Advanced Study Institute Series C: Mathematical and Physical Sciences, vol. 62, D. Reidel Publishing Co., Dordrecht-Boston, Mass., 1980. MR 608990
Paul R. Chernoff and Jerrold E. Marsden, Properties of infinite dimensional Hamiltonian systems, Lecture Notes in Mathematics, Vol. 425, Springer-Verlag, Berlin-New York, 1974. MR 0650113
14. P. Chernoff and J. Marsden, Review of "Lie algebras and quantum mechanics" and "Vector bundles in mathematical physics" by Robert Hermann, Bull. Amer. Math. Soc. 79(1973), 1150-1162.
P. E. Crouch, Dynamical realizations of finite Volterra series, SIAM J. Control Optim. 19 (1981), no. 2, 177–202. MR 605615, DOI 10.1137/0319014
M. Daniel and C.-M. Viallet, The geometrical setting of gauge theories of the Yang-Mills type, Rev. Modern Phys. 52 (1980), no. 1, 175–197. MR 553409, DOI 10.1103/RevModPhys.52.175
Egbert Dierker, Topological methods in Walrasian economics, Lecture Notes in Economics and Mathematical Systems, Vol. 92, Springer-Verlag, Berlin-New York, 1974. MR 0378736
J. Dieudonné, Treatise on analysis. Vol. IV, Pure and Applied Mathematics, Vol. 10-IV, Academic Press, New York-London, 1974. Translated by I. G. Macdonald. MR 0362066
A. Böhm and J. D. Dollard (eds.), Fiber bundle techniques in gauge theories, Lecture Notes in Physics, Vol. 67, Springer-Verlag, Berlin-New York, 1977. Lectures in Mathematical Physics held at the University of Texas at Austin, Austin, Tex., 1976–1977. MR 0443737
E. J. Flaherty, Hermitian and Kählerian geometry in relativity, Lecture Notes in Physics, Vol. 46, Springer-Verlag, Berlin-New York, 1976. MR 0411532
Edward J. Flaherty Jr., Complex variables in relativity, General relativity and gravitation, Vol. 2, Plenum, New York-London, 1980, pp. 207–239. MR 617921
Theodore Frankel, Gravitational curvature, W. H. Freeman and Co., San Francisco, Calif., 1979. An introduction to Einstein’s theory. MR 518868
23. F. R. Gantmacher, The theory of matrices, Vol. 2, Chelsea, New York, 1959.
R. C. Gunning, Lectures on vector bundles over Riemann surfaces, University of Tokyo Press, Tokyo; Princeton University Press, Princeton, N.J., 1967. MR 0230326
Victor Guillemin and Shlomo Sternberg, Geometric asymptotics, Mathematical Surveys, No. 14, American Mathematical Society, Providence, R.I., 1977. MR 0516965
S. W. Hawking and G. F. R. Ellis, The large scale structure of space-time, Cambridge Monographs on Mathematical Physics, No. 1, Cambridge University Press, London-New York, 1973. MR 0424186
G. W. Haynes and H. Hermes, Nonlinear controllability via Lie theory, SIAM J. Control 8 (1970), 450–460. MR 0277859
Robert Hermann, Algebraic topics in systems theory, Interdisciplinary Mathematics, III, Robert Hermann, Department of Mathematics, Rutgers University, New Brunswick, N.J., 1973. (Algebra, applied to physics and systems theory, Part III). MR 0504083
Robert Hermann, On the accessibility problem in control theory, Internat. Sympos. Nonlinear Differential Equations and Nonlinear Mechanics, Academic Press, New York, 1963, pp. 325–332. MR 0149402
Robert Hermann, Vector bundles in mathematical physics. Vols. I, II, W. A. Benjamin, Inc., New York, 1970. MR 0266551
Robert Hermann and Arthur J. Krener, Nonlinear controllability and observability, IEEE Trans. Automatic Control AC-22 (1977), no. 5, 728–740. MR 0476017, DOI 10.1109/tac.1977.1101601
Robert Hermann and Clyde F. Martin, Applications of algebraic geometry to systems theory. I, IEEE Trans. Automatic Control AC-22 (1977), no. 1, 19–25. MR 0444172, DOI 10.1109/tac.1977.1101395
33. R. Hermann, Review of "Elements of soliton theory" by G. L. Lamb, Jr., Bull. Amer. Math. Soc. (N. S.) 5 (1981), 203-209.
H. Hermes, On local and global controllability, SIAM J. Control 12 (1974), 252–261. Collection of articles dedicated to the memory of Lucien W. Neustadt. MR 0451293
Ronald M. Hirschorn, Controllability in nonlinear systems, J. Differential Equations 19 (1975), no. 1, 46–61. MR 431271, DOI 10.1016/0022-0396(75)90017-0
Ronald M. Hirschorn, Invertibility of control systems on Lie groups, SIAM J. Control Optim. 15 (1977), no. 6, 1034–1049. MR 527880, DOI 10.1137/0315067
R. M. Hirschorn, $(A,\,{\cal B})$-invariant distributions and disturbance decoupling of nonlinear systems, SIAM J. Control Optim. 19 (1981), no. 1, 1–19. MR 603076, DOI 10.1137/0319001
Velimir Jurdjevic and Héctor J. Sussmann, Control systems on Lie groups, J. Differential Equations 12 (1972), 313–329. MR 331185, DOI 10.1016/0022-0396(72)90035-6
V. Jurdjevic and I. Kupka, Control systems subordinated to a group action: accessibility, J. Differential Equations 39 (1981), no. 2, 186–211. MR 607781, DOI 10.1016/0022-0396(81)90072-3
R. E. Kalman, Kronecker invariants and feedback, Ordinary differential equations (Proc. NRL-MRC Conf., Math. Res. Center, Naval Res. Lab., Washington, D.C., 1971) Academic Press, New York, 1972, pp. 459–471. MR 0421751
Bertram Kostant, Quantization and unitary representations. I. Prequantization, Lectures in modern analysis and applications, III, Lecture Notes in Math., Vol. 170, Springer, Berlin, 1970, pp. 87–208. MR 0294568
Arthur J. Krener, A decomposition theory for differentiable systems, SIAM J. Control Optim. 15 (1977), no. 5, 813–829. MR 479481, DOI 10.1137/0315052
Alberto Isidori, Arthur J. Krener, Claudio Gori-Giorgi, and Salvatore Monaco, Nonlinear decoupling via feedback: a differential geometric approach, IEEE Trans. Automat. Control 26 (1981), no. 2, 331–345. MR 613540, DOI 10.1109/TAC.1981.1102604
D. E. Lerner and P. D. Sommers (eds.), Complex manifold techniques in theoretical physics, Research Notes in Mathematics, vol. 32, Pitman (Advanced Publishing Program), Boston, Mass.-London, 1979. MR 564439
Claude Lobry, Contrôlabilité des systèmes non linéaires, SIAM J. Control 8 (1970), 573–605 (French). MR 0271979
46. S. Mac Lane, Geometrical mechanics (2 parts), Dept. of Math., Univ. of Chicago, Illinois, 1968.
J. Marsden, Application of global analysis in mathematical physics, Carleton Mathematical Lecture Notes, No. 3, Carleton University, Department of Mathematics, Ottawa, Ont., 1973. MR 0646466
Clyde F. Martin and Robert Hermann, Applications of algebraic geometry to systems theory. II. Feedback and pole placement for linear Hamiltonian systems, Proc. IEEE 65 (1977), no. 6, 841–848. MR 0527293
Clyde F. Martin and Robert Hermann, Applications of algebraic geometry to systems theory. II. Feedback and pole placement for linear Hamiltonian systems, Proc. IEEE 65 (1977), no. 6, 841–848. MR 0527293
50. D. Q. Mayne and R. W. Brockett (Editors), Geometric methods in systems theory, Reidel, Dordrecht, Holland, 1973.
N. D. Mermin, The topological theory of defects in ordered media, Rev. Modern Phys. 51 (1979), no. 3, 591–648. MR 541885, DOI 10.1103/RevModPhys.51.591
Charles W. Misner, Kip S. Thorne, and John Archibald Wheeler, Gravitation, W. H. Freeman and Co., San Francisco, Calif., 1973. MR 0418833
A. I. Murdoch and H. Cohen, Symmetry considerations for material surfaces, Arch. Rational Mech. Anal. 72 (1979/80), no. 1, 61–98. MR 540222, DOI 10.1007/BF00250737
Walter Noll, Materially uniform simple bodies with inhomogeneities, Arch. Rational Mech. Anal. 27 (1967/68), 1–32. MR 225530, DOI 10.1007/BF00276433
B. N. Parlett and W. G. Poole Jr., A geometric theory for the $\textrm {QR},\,\textrm {LU}$ and power iterations, SIAM J. Numer. Anal. 10 (1973), 389–412. MR 336979, DOI 10.1137/0710035
R. Penrose and R. S. Ward, Twistors for flat and curved space-time, General relativity and gravitation, Vol. 2, Plenum, New York-London, 1980, pp. 283–328. MR 617923
V. Poénaru, Some aspects of the theory of defects of ordered media and gauge fields related to foliations, Comm. Math. Phys. 80 (1981), no. 1, 127–136. MR 623154
Rainer Kurt Sachs and Hung Hsi Wu, General relativity for mathematicians, Graduate Texts in Mathematics, Vol. 48, Springer-Verlag, New York-Heidelberg, 1977. MR 0503498
C. R. Schneider, Global aspects of the matrix Riccati equation, Math. Systems Theory 7 (1973), no. 3, 281–286. MR 391175, DOI 10.1007/BF01795945
David J. Simms and Nicholas M. J. Woodhouse, Lectures in geometric quantization, Lecture Notes in Physics, vol. 53, Springer-Verlag, Berlin-New York, 1976. MR 0672639
Jędrzej Śniatycki, Geometric quantization and quantum mechanics, Applied Mathematical Sciences, vol. 30, Springer-Verlag, New York-Berlin, 1980. MR 554085
62. C. P. Snow, The search, 2nd ed., Schribner, New York, 1958, pp. 203-209.
J.-M. Souriau, Structure des systèmes dynamiques, Dunod, Paris, 1970 (French). Maîtrises de mathématiques. MR 0260238
Shlomo Sternberg, Lectures on differential geometry, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964. MR 0193578
65. S. Sternberg, Review of "Foundations of mechanics" by Ralph Abraham and Jerrold E. Marsden, Bull. Amer. Math. Soc. (N. S.) 2 (1980), 378-387.
Héctor J. Sussmann and Velimir Jurdjevic, Controllability of nonlinear systems, J. Differential Equations 12 (1972), 95–116. MR 338882, DOI 10.1016/0022-0396(72)90007-1
Hector J. Sussmann, Existence and uniqueness of minimal realizations of nonlinear systems, Math. Systems Theory 10 (1976/77), no. 3, 263–284. MR 437158, DOI 10.1007/BF01683278
Héctor J. Sussmann, Subanalytic sets and feedback control, J. Differential Equations 31 (1979), no. 1, 31–52. MR 524816, DOI 10.1016/0022-0396(79)90151-7
Walter Thirring, A course in mathematical physics. Vol. I. Classical dynamical systems, Springer-Verlag, New York-Vienna, 1978. Translated from the German by Evans M. Harrell. MR 507189
Walter Thirring, Lehrbuch der mathematischen Physik. Band 2, Springer-Verlag, Vienna, 1978 (German). Klassische Feldtheorie. MR 496192
Andrzej Trautman, Fiber bundles, gauge fields, and gravitation, General relativity and gravitation, Vol. 1, Plenum, New York-London, 1980, pp. 287–308. MR 583721
Nolan R. Wallach, Symplectic geometry and Fourier analysis, Lie Groups: History, Frontiers and Applications, Vol. V, Math Sci Press, Brookline, Mass., 1977. With an appendix on quantum mechanics by Robert Hermann. MR 0488148
C.-C. Wang, On the geometric structures of simple bodies. A mathematical foundation for the theory of continuous distributions of dislocations, Arch. Rational Mech. Anal. 27 (1967/68), 33–94. MR 229420, DOI 10.1007/BF00276434
L. P. Hughston and Richard Samuel Ward (eds.), Advances in twistor theory, Research Notes in Mathematics, vol. 37, Pitman (Advanced Publishing Program), Boston, Mass.-London, 1979. MR 578487
R. O. Wells Jr., Complex manifolds and mathematical physics, Bull. Amer. Math. Soc. (N.S.) 1 (1979), no. 2, 296–336. MR 520077, DOI 10.1090/S0273-0979-1979-14596-8
Alan Weinstein, Lectures on symplectic manifolds, Regional Conference Series in Mathematics, No. 29, American Mathematical Society, Providence, R.I., 1977. Expository lectures from the CBMS Regional Conference held at the University of North Carolina, March 8–12, 1976. MR 0464312
W. Murray Wonham, Linear multivariable control: a geometric approach, 2nd ed., Applications of Mathematics, vol. 10, Springer-Verlag, New York-Berlin, 1979. MR 569358
- 1.
- R. Abraham and J. Marsden, Foundations of mechanics, 2nd ed., Benjamin-Cummings, Reading, Mass., 1978. MR 0515141
- 2.
- V. I. Arnold, Mathematical methods of classical mechanics, Graduate Texts in Math., No. 60, Springer-Verlag, New York, 1978. MR 690288
- 3.
- K. Bleuler and A. Reetz (Editors), Differential geometric methods in mathematical physics. I, Lecture Notes in Math., vol. 570, Springer-Verlag, Berlin-Heidelberg, 1977. MR 434688
- 4.
- K. Bleuler, H. R. Petry and A. Reetz (Editors), Differential geometric methods in mathematical physics. II, Lecture Notes in Math., vol. 676, Springer-Verlag, Berlin-Heidelberg, 1978. MR 519605
- 5.
- F. Bloom, Modern differential geometric techniques in the theory of continuous distributions of dislocations, Lecture Notes in Math., vol. 733, Springer-Verlag, Berlin, 1979. MR 546839
- 6.
- R. W. Brockett, Finite dimensional linear systems, Wiley, New York, 1969.
- 7.
- R. W. Brockett, Systems theory on group manifolds and coset spaces, SIAM J. Control Optim. 10 (1972), 265-284. MR 315559
- 8.
- R. W. Brockett, Lie theory and control systems defined on spheres, SIAM J. Appl. Math. 25 (1973), 213-225. MR 327337
- 9.
- R. W. Brockett, Nonlinear systems and differential geometry, Proc. of the IEEE 64 (1976), 61-72. MR 432255
- 10.
- P. Brunovsky, A classification of linear controllable systems, Kybernetika (Prague) 6 (3), 1970, 173-188. MR 284247
- 11.
- C. I. Byrnes (Editor), Partial differential equations and geometry, Proc. Park City Conf., Lecture Notes in Pure and Appl. Math., Vol. 48, Marcel Dekker, 1979. MR 535586
- 12.
- C. I. Byrnes and C. F. Martin (Editors), Geometrical methods for the theory of linear systems, NATO Advanced Study Institutes Series D, Reidel, Dordrecht, Holland, 1980. MR 608990
- 13.
- P. Chernoff and J. Marsden, Properties of infinite dimensional Hamiltonian systems, Lecture Notes in Math., vol. 425, Springer-Verlag, New York, 1974. MR 650113
- 14.
- P. Chernoff and J. Marsden, Review of "Lie algebras and quantum mechanics" and "Vector bundles in mathematical physics" by Robert Hermann, Bull. Amer. Math. Soc. 79(1973), 1150-1162.
- 15.
- P. E. Crouch, Dynamical realizations of finite Volterra series, SIAM J. Control Optim. 19 (1981), 177-202. MR 605615
- 16.
- M. Daniel and C. M. Viallet, The geometrical setting of gauge theories of the Yang-Mills type, Rev. Modern Phys. 52 (1980), 175-197. MR 553409
- 17.
- E. Dierker, Topological methods in Walrasian economics, Lecture Notes in Economics and Systems, No. 92, Springer-Verlag, Berlin, 1970. MR 378736
- 18.
- J. Dieudonné, Treatise on analysis, vol. 10-IV, Academic Press, New York, 1974. MR 362066
- 19.
- W. Drechsler and M. E. Mayer, Fiber bundle techniques in gauge theories, Lecture Notes in Physics, No. 67, Springer-Verlag, Berlin-Heidelberg, 1977. MR 443737
- 20.
- E. J. Flaherty, Hermitian and Kählerian geometry in relativity, Lecture Notes in Phys., No. 46, Springer-Verlag, Berlin-Heidelberg, 1976. MR 411532
- 21.
- E. J. Flaherty, Complex variables in relativity, General Relativity and Gravitation, Vol. 2 (A. Held, ed.), Plenum Press, New York, 1980, pp. 207-239. MR 617921
- 22.
- T. Frankel, Gravitational curvature, an introduction to Einstein's theory, Freeman, San Francisco, 1979. MR 518868
- 23.
- F. R. Gantmacher, The theory of matrices, Vol. 2, Chelsea, New York, 1959.
- 24.
- R. Gunning, Lectures on vector bundles over Riemann surfaces, Princeton Univ. Press, Princeton, N. J., 1967. MR 230326
- 25.
- V. Guillemin and S. Sternberg, Geometric asymptotics, Math. Surveys, no. 14, Amer. Math. Soc. Providence, R. I., 1977. MR 516965
- 26.
- S. W. Hawking and G. F. R. Ellis, The large scale structure of space-time, Cambridge Univ. Press, London and New York, 1973. MR 424186
- 27.
- G. W. Haynes and H. Hermes, Nonlinear controllability via Lie theory, SIAM J. Control Optim. 8 (1970), 450-460. MR 277859
- 28.
- R. Hermann, Algebraic topics in systems theory, Interdisciplinary Mathematics, Vol. 3, Math-Sci Press, Brookline, Mass., 1973. MR 504083
- 29.
- R. Hermann, On the accessibility problem in control theory, International Symposium on Nonlinear Differential Equations and Nonlinear Mechanics, Academic Press, New York, 1963, pp. 325-332. MR 149402
- 30.
- R. Hermann, Vector bundles in mathematical physics, vol. 1, Benjamin, New York, 1970. MR 266551
- 31.
- R. Hermann and A. J. Krener, Nonlinear controllability and observability, IEEE Trans. Autom. Control. AC-22 (1977), 728-740. MR 476017
- 32.
- R. Hermann and C. F. Martin, Applications of algebraic geometry to systems theory--Part I, IEEE Trans. Automat. Control AC-22 (1977), 19-25. MR 444172
- 33.
- R. Hermann, Review of "Elements of soliton theory" by G. L. Lamb, Jr., Bull. Amer. Math. Soc. (N. S.) 5 (1981), 203-209.
- 34.
- H. Hermes, On local and global controllability, SIAM J. Control Optim. 12 (1974), 252-261. MR 451293
- 35.
- R. M. Hirschorn, Controllability in nonlinear systems, J. Differential Equations 19 (1975), 46-61. MR 431271
- 36.
- R. M. Hirschorn, Invertibility of control systems on Lie groups, SIAM J. Control Optim. 15 (1977), 1034-1049. MR 527880
- 37.
- R. M. Hirschorn, (A, B)-invariant distributions and disturbance decoupling of nonlinear systems, SIAM J. Control Optim. 19 (1981), 1-19. MR 603076
- 38.
- V. Jurdjevic and H. J. Sussmann, Control systems on Lie groups, J. Differential Equations 12 (1972), 313-329. MR 331185
- 39.
- V. Jurdjevic and I. Kupka, Control systems subordinated to a group action: Accessibility, J. Differential Equations 39 (1981), 186-211. MR 607781
- 40.
- R. E. Kalman, Kronecker invariants and feedback, Conf. Ordinary Differential Equations (NRL Mathematics Research Center, June 14-23, 1971), Ordinary Differential Equations (C. Weiss, ed.), Academic Press, New York, 1972, pp. 459-471. MR 421751
- 41.
- B. Kostant, Quantization and unitary representations, Lecture Notes in Math., vol. 170, Springer-Verlag, New York, 1970. MR 294568
- 42.
- A. J. Krener, A decomposition theory for differentiable systems, SIAM J. Control Optim. 15 (1977), 813-829. MR 479481
- 43.
- A. J. Krener, A. Isidori, C. Gori-Giorgi and S. Monaco, Nonlinear decoupling via feedback: A differential geometric approach, IEEE Trans. Automat. Control, AC-26 (1981), 331-345. MR 613540
- 44.
- D. E. Lerner and P. D. Sommers (Editors), Complex manifold techniques in theoretical physics, Pitman Advanced Publishing Program, London, 1979; Research Notes in Math. 32. MR 564439
- 45.
- C. Lobry, Controlabilite des systemes non lineaires, SIAM J. Control Optim. 8 (1970), 573-605. MR 271979
- 46.
- S. Mac Lane, Geometrical mechanics (2 parts), Dept. of Math., Univ. of Chicago, Illinois, 1968.
- 47.
- J. Marsden, Applications of global analysis in mathematical physics, Publish or Perish, Boston, 1974. MR 646816
- 48.
- C. F. Martin and R. Hermann, Applications of algebraic geometry to systems theory. Part II: Feedback and pole placement for linear Hamiltonian systems, Proc. of the IEEE 65 (1977), 841-848. MR 527293
- 49.
- C. F. Martin and R. Hermann, Applications of algebraic geometry to systems theory: The McMillan degree and Kronecker indices of transfer functions as topological and holomorphic system invariants, SIAM J. Control Optim. 16 (1978), 743-755. MR 527294
- 50.
- D. Q. Mayne and R. W. Brockett (Editors), Geometric methods in systems theory, Reidel, Dordrecht, Holland, 1973.
- 51.
- N. D. Mermin, The topological theory of defects in ordered media, Rev. Modern Phys. 51 (1979), 591-648. MR 541885
- 52.
- C. Misner, K. Thorne and J. A. Wheeler, Gravitation, Freeman, San Francisco, 1973. MR 418833
- 53.
- A. I. Murdoch and H. Cohen, Symmetry considerations for material surfaces, Arch. Rational Mech. Anal. 72 (1979), 61-98. MR 540222
- 54.
- W. Noll, Materially uniform simple bodies with inhomogeneitics, Arch. Rational Mech. Anal. 27(1967), 1-32. MR 225530
- 55.
- B. N. Parlett and W. G. Poole, Jr., A geometric theory for the QR, LU and power iterations, SIAM J. Numer. Anal. 10 (1973), 389-412. MR 336979
- 56.
- R. Penrose and R. S. Ward, Twisters for flat and curved space-time, General Relativity and Gravitation, Vol. 2 (A. Held, ed.), Plenum Press, New York, 1980, pp. 283-328. MR 617923
- 57.
- V. Poénaru, Some aspects of the theory of defects of ordered media and gauge fields related to foliations, Comm. Math. Phys. 80(1981), 127-136. MR 623154
- 58.
- R. Sachs and H. Wu, General relativity for mathematicians, Graduate Texts in Math., No. 48, Springer-Verlag, Berlin-Heidelberg and New York, 1977. MR 503498
- 59.
- C. R. Schneider, Global aspects of the matrix Riccati equation, Math. Systems Theory 7 (1973), 281-286. MR 391175
- 60.
- D. J. Simms and N. M. J. Woodhouse, Lectures on geometric quantization, Lecture Notes in Phys., No. 53, Springer-Verlag, Berlin-Heidelberg, 1976. MR 672639
- 61.
- J. Sniatycki, Geometric quantization and quantum mechanics, Applied Mathematical Sciences Series, No. 30, Springer-Verlag, New York, 1980. MR 554085
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- C. P. Snow, The search, 2nd ed., Schribner, New York, 1958, pp. 203-209.
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- J. M. Souriau, Structure des systemes dynamiques, Dunod, Paris, 1970. MR 260238
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- S. Sternberg, Lectures on differential geometry, Prentice-Hall, Englewood Cliffs, N. J., 1963. MR 193578
- 65.
- S. Sternberg, Review of "Foundations of mechanics" by Ralph Abraham and Jerrold E. Marsden, Bull. Amer. Math. Soc. (N. S.) 2 (1980), 378-387.
- 66.
- H. J. Sussmann and V. Jurdjevic, Controllability of nonlinear systems, J. Differential Equations 12 (1972), 95-116. MR 338882
- 67.
- H. J. Sussmann, Existence and uniqueness of minimal realizations of nonlinear systems, Math. Systems Theory 10 (1977), 263-284. MR 437158
- 68.
- H. J. Sussmann, Subanalytic sets and feedback control, J. Differential Equations 31 (1979), 31-52. MR 524816
- 69.
- W. Thirring, A course in mathematical physics. I, Classical dynamical systems, Springer-Verlag, New York, 1978. MR 507189
- 70.
- W. Thirring, A course in mathematical physics. II, Classical field theory, Springer-Verlag, New York, 1979. MR 553112
- 71.
- A. Trautman, Fiber bundles, gauge fields and gravitation, General Relativity and Gravitation, Vol. 1 (A. Held, ed.), Plenum Press, New York, 1980, pp. 287-308. MR 583721
- 72.
- N. R. Wallach, Symplectic geometry and Fourier analysis, Lie Groups: History, Frontiers and Applications, Vol. V, Math-Sci Press, Brookline, Mass., 1977. MR 488148
- 73.
- C. -C. Wang, On the geometric structures of simple bodies, a mathematical foundation for the theory of continuous distributions of dislocations, Arch. Rational Mech. Anal. 27 (1967), 33-94. MR 229420
- 74.
- R. S. Ward and L. P. Hughston (Editors), Advances in twistor theory, Pitman Advanced Publishing Program, London, 1979; Research Notes in Math. 37. MR 578487
- 75.
- R. O. Wells, Complex manifolds and mathematical physics, Bull. Amer. Math. Soc. (N. S.) 1 (1979), 296-336. MR 520077
- 76.
- A. Weinstein, Lectures on symplectic manifolds, CBMS Conf. Ser. in Math., No. 29, Amer. Math. Soc., Providence, R. I., 1977. MR 464312
- 77.
- W. M. Wonham, Linear multivariable control: A geometric approach, 2nd ed., Springer-Verlag, New York, 1979. MR 569358
Review Information:
Reviewer:
Clark R. Givens
Reviewer:
Richard S. Millman
Journal:
Bull. Amer. Math. Soc.
6 (1982), 467-478
DOI:
https://doi.org/10.1090/S0273-0979-1982-15019-4