The Mathematical Heritage of Henri Poincar

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Felix E. Browder
American Mathematical Soc., Dec 31, 1983 - Mathematics - 470 pages
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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.
 

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Contents

PART
3
Web geometry
11
the first 150 years
25
Periodic solutions of nonlinear vibrating strings and duality principles
31
Completeness of the KahlerEinstein metric on bounded domains and
41
Symplectic geometry
47
Fixed point theory and nonlinear problems
49
Graeme Segals Burnside ring conjecture
77
The fundamental theorem of algebra and complexity theory
155
Poincaré and Lie groups
157
Discrete conformal groups and measurable dynamics
169
Several complex variables
189
Poincaré recurrence and number theory
193
The ergodic theoretical proof of Szemerédis theorem
217
Poincaré and topology
245
Résumé analytique
257

Three dimensional manifolds Kleinian groups and hyperbolic geometry
87
Variational and topological methods in nonlinear problems
89
Riemann surfaces discontinuous groups and Lie groups
115
the need of Plancks constant
127
Difierentiable dynamical systems and the problem of turbulence
141
Loeuvre mathématique de Poincaré
359
Lettre de M Pierre Boutroux a M MittagLeflier
441
Bibliography of Henri Poincaré
447
Books and articles about Poincaré
467
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