Bulletin of the American Mathematical Society

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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

62.

C. P. Snow, The search, 2nd ed., Schribner, New York, 1958, pp. 203-209.

63.

J. M. Souriau, Structure des systemes dynamiques, Dunod, Paris, 1970. MR 260238

64.

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