Proceedings of Symposia in Pure Mathematics 1983; 905 pp; softcover Volume: 39 Reprint/Revision History: reprinted with corrections to Part 1, 1984 ISBN10: 0821814427 ISBN13: 9780821814420 List Price: US$119 Member Price: US$95.20 Order Code: PSPUM/39
 On April 710, 1980, the American Mathematical Society sponsored a Symposium on the Mathematical Heritage of Henri Poincaré, held at Indiana University, Bloomington, Indiana. This volume presents the written versions of all but three of the invited talks presented at this Symposium (those by W. Browder, A. Jaffe, and J. Mather were not written up for publication). In addition, it contains two papers by invited speakers who were not able to attend, S. S. Chern and L. Nirenberg. If one traces the influence of Poincaré through the major mathematical figures of the early and midtwentieth century, it is through American mathematicians as well as French that this influence flows, through G. D. Birkhoff, Solomon Lefschetz, and Marston Morse. This continuing tradition represents one of the major strands of American as well as world mathematics, and it is as a testimony to this tradition as an opening to the future creativity of mathematics that this volume is dedicated. Table of Contents Part 1. Section 1, Geometry  S.S. Chern  Web geometry
 J.I. Igusa  Problems on abelian functions at the time of Pincaré and some at present
 J. Milnor  Hyperbolic geometry: The first 150 years
 N. Mok and S.T. Yau  Completeness of the KählerEinstein metric on bounded domains and the characterization of domains of holomorphy by curvature conditions
 A. Weinstein  Symplectic geometry
Section 2, Topology  J. F. Adams  Graeme Segal's Burnside ring conjecture
 W. P. Thurston  Three dimensional manifolds, Kleinian groups and hyperbolic geometry
Section 3, Riemann surfaces, discontinuous groups and Lie groups  L. Bers  Finite dimesnional Teichmüller spaces and generalizations
 W. Schmid  Poincaré and Lie groups
 D. Sullican  Discrete conformal groups and measurable dynamics
Section 4, Several complex variables  M. Beals, C. Fefferman, and R. Grossman  Strictly pseudoconvex domains in \(\mathbf C^n\)
 P. A. Griffiths  Poincaré and algebraic geometry
 R. Penrose  Physical spacetime and nonrealizable CRstructures
 R. O. Wells, Jr.  The CauchyRiemann equations and differential geometry
Part 2. Section 5, Topological methods in nonlinear problems  R. Bott  Lectures on Morse theory, old and new
 H. Brezis  Periodic solutions of nonlinear vibrating strings and duality principles
 F. E. Browder  Fixed point theory and nonlinear problems
 L. Nirenberg  Variational and topological methods in nonlinear problems
Section 6, Mechanics and dynamical systems  J. Leray  The meaning of Maslov's asymptotic method: The need of Planck's constant in mathematics
 D. Ruelle  Differentiable dynamical systems and the problem of turbulence
 S. Smale  The fundamental theorem of algebra and complexity theory
Section 7, Ergodic theory and recurrence  H. Furstenberg  Poincaré recurrence and number theory
 H. Furstenberg, Y. Katznelson, and D. Ornstein  The ergodic theoretical proof of Szemerédi's theorem
Section 8, Historical material  P. S. Aleksandrov  Poincaré and topology
 H. Poincaré  Résumé analytique
 J. Hadamard  L'oeuvre mathématique de Poincaré
 Lettre de M. Pierre Boutroux à M. MittagLeffler
 Bibliography of Henri Poincaré
 Books and articles about Poincaré
