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.
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