The mathematical heritage of Henri Poincaré

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書誌事項

The mathematical heritage of Henri Poincaré

[edited by Felix E. Browder ; prepared by the American Mathematical Society, with partial support from National Science Foundation grant mCS 79-22916]

（Proceedings of symposia in pure mathematics, v. 39）

American Mathematical Society, 1983

  • : set
  • pt. 1
  • pt. 2

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注記

"Proceedings of the Symposium on the Mathematical Heritage of Henri Poincaré, held at Indiana University, Bloomington, Indiana, April 7-10, 1980"--T.p. verso

"Bibliography of Henri Poincaré": pt. 2, p. 447-466

"Books and articles about Poincaré": pt. 2, p. 467-470

Includes bibliographies

内容説明・目次

巻冊次

: set ISBN 9780821814420

内容説明

On April 7-10, 1980, the American Mathematical Society sponsored a Symposium on the Mathematical Heritage of Henri Poincare, 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 Poincare 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.

目次

Part 1. Section 1, Geometry: Web geometry by S.-S. Chern Problems on abelian functions at the time of Pincare and some at present by J.-I. Igusa Hyperbolic geometry: The first 150 years by J. Milnor Completeness of the Kahler-Einstein metric on bounded domains and the characterization of domains of holomorphy by curvature conditions by N. Mok and S.-T. Yau Symplectic geometry by A. Weinstein Section 2, Topology: Graeme Segal's Burnside ring conjecture by J. F. Adams Three dimensional manifolds, Kleinian groups and hyperbolic geometry by W. P. Thurston Section 3, Riemann surfaces, discontinuous groups and Lie groups: Finite dimensional Teichmuller spaces and generalizations by L. Bers Poincare and Lie groups by W. Schmid Discrete conformal groups and measurable dynamics by D. Sullican Section 4, Several complex variables: Strictly pseudoconvex domains in $\mathbf C^n$ by M. Beals, C. Fefferman, and R. Grossman Poincare and algebraic geometry by P. A. Griffiths Physical space-time and nonrealizable CR-structures by R. Penrose The Cauchy-Riemann equations and differential geometry by R. O. Wells, Jr. Part 2. Section 5, Topological methods in nonlinear problems: Lectures on Morse theory, old and new by R. Bott Periodic solutions of nonlinear vibrating strings and duality principles by H. Brezis Fixed point theory and nonlinear problems by F. E. Browder Variational and topological methods in nonlinear problems by L. Nirenberg Section 6, Mechanics and dynamical systems: The meaning of Maslov's asymptotic method: The need of Planck's constant in mathematics by J. Leray Differentiable dynamical systems and the problem of turbulence by D. Ruelle The fundamental theorem of algebra and complexity theory by S. Smale Section 7, Ergodic theory and recurrence: Poincare recurrence and number theory by H. Furstenberg The ergodic theoretical proof of Szemeredi's theorem by H. Furstenberg, Y. Katznelson, and D. Ornstein Section 8, Historical material: Poincare and topology by P. S. Aleksandrov Resume analytique by H. Poincare L'oeuvre mathematique de Poincare by J. Hadamard Lettre de M. Pierre Boutroux a M. Mittag-Leffler Bibliography of Henri Poincare Books and articles about Poincare.
巻冊次

pt. 1 ISBN 9780821814482

内容説明

On April 7-10, 1980, the American Mathematical Society sponsored a Symposium on the Mathematical Heritage of Henri Poincari, 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 Poincari 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. This part contains sections on geometry, topology, Riemann surfaces, discontinuous groups and Lie groups, and several complex variables.
巻冊次

pt. 2 ISBN 9780821814499

内容説明

On April 7-10, 1980, the American Mathematical Society sponsored a Symposium on the Mathematical Heritage of Henri Poincari, 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 Poincari 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. This part contains sections on topological methods in nonlinear problems, mechanics and dynamical systems, ergodic theory and recurrence, and historical material.

目次

  • Periodic solutions of nonlinear vibrating strings and duality principles
  • Fixed point theory and nonlinear problems
  • Variational and topological methods in nonlinear problems
  • Differentiable dynamical systems and the problem of turbulence
  • The fundamental theorem of algebra and complexity theory
  • The ergodic theoretical proof of Szemeredi's theorem
  • Resume analytique
  • L'oeuvre mathematique de Poincare
  • Lettre de M. Pierre Boutroux a M. Mittag-Leffler
  • Bibliography of Henri Poincare
  • Books and articles about Poincare

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