The Mathematical Heritage of Henri Poincare, Part 2On 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
| 3 | |
| 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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Common terms and phrases
abéliennes Acad algebraic algébriques analogue autre avait Banach space bifurcation C’est cl(G coefficients compact condition converges convex courbes critical point d’abord d’autres d’une defined degree function degree theory deux développement diffeomorphisms differential equations donnée dynamical system eigenvalues équations différentielles equivariant ergodic ergodic theory été être exemple exists fait finite-dimensional follows fonctions fonctions fuchsiennes général geodesic Hamiltonian Hamiltonian systems Hence Henri Poincaré Hilbert space homotopy intégrales invariant j’ai l’équation l’étude l’on Lagrangian Lemma linéaires manifold maps f Math mathematical mathématique Mécanique méthode monotone Morse Morse theory n’est Navier-Stokes equation nombre nondegenerate nonlinear nontrivial nouvelles Oeuvres particulier periodic solutions peut POINCARÉ point de vue points singuliers polynomial premier problem proof of Theorem PROPOSITION propriétés prove pseudo-monotone qu’elle qu’il qu’on qu’une quelconque recurrent résultats séries seule solutions périodiques stationary point subset Suppose théorème tion topological tout unstable manifolds valeurs variables zero
Bibliographic information
| Title | The Mathematical Heritage of Henri Poincare, Part 2 Proceedings of symposia in pure mathematics Part 2 of The Mathematical Heritage of Hen The Mathematical Heritage of Henri Poincaré Part 2 of The mathematical heritage of Henri Poincaré: Proceedings of the Symposium on the mathematical heritage of Henri Poincaré held at Indiana University Bloomington, Indiana, April 7-10, 1980 |
| Editor | Felix E. Browder |
| Edition | reprint |
| Publisher | American Mathematical Soc., 1983 |
| ISBN | 0821814494, 9780821814499 |
| Length | 470 pages |
| Subjects | › Mathematics / History & Philosophy |
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