VI CONTENTS Poincare and algebraic geometry By PHILLIP A. GRIFFITHS 387 Physical space-time and nonrealizable CR-structures By ROGE R PENROSE 401 The Cauchy-Riemann equations and differential geometry By R. O. WELLS, J R 423 PART 2 Section 5. Topological methods in nonlinear problems Lectures on Morse theory, old and new By RAOUL BOTT 3 Periodic solutions of nonlinear vibrating strings and duality principles By HAIM BREZIS 31 Fixed point theory and nonlinear problems By FELIX E. BROWDER 49 Variational and topological methods in nonlinear problems By L. NIRENBERG 89 Section 6. Mechanics and dynamical systems The meaning of Maslov's asymptotic method: the need of Planck's constant in mathematics By JEAN LERAY 127 Dififerentiable dynamical systems and the problem of turbulence By DAVID RUELLE 141 The fundamental theorem of algebra and complexity theory By STEVE SMALE 155 Section 7. Ergodic theory and recurrence Poincare recurrence and number theory By HARRY FURSTENBERG 193 The ergodic theoretical proof of Szemeredi's theorem By H. FURSTENBERG, Y. KATZNELSON AND D. ORNSTEIN 217 Section 8. Historical material Poincare and topology By P. S. ALEKSANDROV 245 Resume analytique By HENRI POINCARE 257 L'oeuvre mathematique de Poincare By JACQUES HADAMARD 359 Lettre de M. Pierre Boutroux a M. Mittag-Leffler 441 Bibliography of Henri Poincare 447 Books and articles about Poincare 467

Purchased from American Mathematical Society for the exclusive use of nofirst nolast (email unknown) Copyright 1983 American Mathematical Society. Duplication prohibited. Please report unauthorized use to cust-serv@ams.org. Thank You! Your purchase supports the AMS' mission, programs, and services for the mathematical community.