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The Mathematical Heritage of Henri Poincaré
Edited by: Felix E. Browder, Rutgers University, New Brunswick, NJ

Proceedings of Symposia in Pure Mathematics
1983; 905 pp; softcover
Volume: 39
Reprint/Revision History:
reprinted with corrections to Part 1, 1984
ISBN-10: 0-8218-1442-7
ISBN-13: 978-0-8218-1442-0
List Price: US$119
Member Price: US$95.20
Order Code: PSPUM/39
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On April 7-10, 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 Kähler-Einstein 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 space-time and nonrealizable CR-structures
  • R. O. Wells, Jr. -- The Cauchy-Riemann 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. Mittag-Leffler
  • Bibliography of Henri Poincaré
  • Books and articles about Poincaré
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