This volume clearly reflects Ricardo Mane's legacy, his contribution to mathematics and the diversity of his mathematical intersts. It contains fifteen refereed research papers on thems including Hamiltonian and Lagrangian dynamics, growth rate of the number of geodesics on a compact manifold, one dimensional complex and real dynamics, and bifurcations and singular cycles. This book also contains two famous sets of notes by Ricardo Mane. One is the seminal paper on Lagrangian dynamics that he had prepared for the conference; the other is on the genericity of zero exponents area preserving diffeomorphisms on surfaces when non Anosov.
This book will be of particular interest to researchers and graduate students in mathematics, mechanics and mathematical physics.
Table of Contents
Singular cycles of vector fields On the growth of the number of geodesics joining two points Directional flows and strong recurrence for polygonal billiards A note on one dimensional dynamics associated to singular cycles Central limit theorem for deterministic systems On necessary and sufficient conditions for uiniform integrability of families of Hamiltonian systems The Lyapunov exponents of generic area preserving diffeomorphisms Lagrangian flows: the dynamics of globally minimizing orbits Anosov geodesic flows and twisted symplectic structures Entropy and geodesic arcs on surfaces On measure and Hausdorff dimension of Julia sets for holomorphic Collet-Eckmann maps Stable ergodicity and partial hyperbolicity Sharp zeta functions for smooth interval maps Lyapunov functions and Anosov flows Henon attractors: SBR measures and Dirac measures for sinks Two dimensional generalizations of Haar bases Spaces that won's say no