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Book DetailsProceedings of Symposia in Pure MathematicsVolume: 39; 1983; 470 ppMSC: Primary 00; Secondary 01;
On April 710, 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.This item is also available as part of a set: 
Table of Contents

Topological methods in nonlinear problems

Raoul Bott  Lectures on Morse theory, old and new

Haïm Brezis  Periodic solutions of nonlinear vibrating strings and duality principles

Felix E. Browder  Fixed point theory and nonlinear problems

L. Nirenberg  Variational and topological methods in nonlinear problems

Mechanics and dynamical systems

Jean Leray  The meaning of Maslov’s asymptotic method: The need of Planck’s constant in mathematics

David Ruelle  Differentiable dynamical systems and the problem of turbulence

Steve Smale  The fundamental theorem of algebra and complexity theory

Ergodic theory and recurrence

Harry Furstenberg  Poincaré recurrence and number theory

H. Furstenberg, Y. Katznelson and D. Ornstein  The ergodic theoretical proof of Szemerédi’s theorem

Historical material

P. S. Aleksandrov  Poincaré and topology

Henri Poincaré  Résumé analytique

Jacques Hadamard  L’oeuvre mathématique de Poincaré


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On April 710, 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.

Topological methods in nonlinear problems

Raoul Bott  Lectures on Morse theory, old and new

Haïm Brezis  Periodic solutions of nonlinear vibrating strings and duality principles

Felix E. Browder  Fixed point theory and nonlinear problems

L. Nirenberg  Variational and topological methods in nonlinear problems

Mechanics and dynamical systems

Jean Leray  The meaning of Maslov’s asymptotic method: The need of Planck’s constant in mathematics

David Ruelle  Differentiable dynamical systems and the problem of turbulence

Steve Smale  The fundamental theorem of algebra and complexity theory

Ergodic theory and recurrence

Harry Furstenberg  Poincaré recurrence and number theory

H. Furstenberg, Y. Katznelson and D. Ornstein  The ergodic theoretical proof of Szemerédi’s theorem

Historical material

P. S. Aleksandrov  Poincaré and topology

Henri Poincaré  Résumé analytique

Jacques Hadamard  L’oeuvre mathématique de Poincaré