Dynamics, Ergodic Theory and Geometry [Hardcover]

Surveys, research articles, and commented problems based on a 2004 MRSI research workshop in symplectic geometry, ergodicity, hyperbolic dynamics, and other areas.Surveys and research articles by leading experts cover several areas of dynamical systems that have recently experienced substantial progress, including symplectic geometry; smooth rigidity; hyperbolic, parabolic, and symbolic dynamics; and ergodic theory.Surveys and research articles by leading experts cover several areas of dynamical systems that have recently experienced substantial progress, including symplectic geometry; smooth rigidity; hyperbolic, parabolic, and symbolic dynamics; and ergodic theory.This volume contains surveys and research articles by leading experts in several areas of dynamical systems that have recently experienced substantial progress. Some of the major surveys focus on symplectic geometry; smooth rigidity; hyperbolic, parabolic, and symbolic dynamics; and ergodic theory. Students and researchers in dynamical systems, geometry, and related areas will find this a fascinating look at the state of the art.Foreword; 1. Quantitative symplectic geometry K. CIELIEBAK, HELMUT HOFER, J. LATSCHEV, aND F. SCHLENK; 2. Local rigidity of group actions: past, present, future David Fisher; 3. Le lemme d'OrnsteinWeiss d'apr?s Gromov Fabrice Krieger; 4. Entropy of holomorphic and rational maps: a survey Shmuel Friedland; 5. Causes of stretching of Birkhoff sums and mixing in flows on surfaces Andrey Kochergin; 6. Solenoid functions for hyperbolic sets on surfaces Alberto A. Pinto and David A. Rand; 7. Random walks derived from billiards Renato Feres; 8. An aperiodic tiling using a dynamical system and Beatty sequences Stanley Eigen, Jorge Navarro, and Vidhu S. Prasad; 9. A Halmosvon Neumann theorem for model sets, and almost automorphic dynamical systems E. Arthur Robinson Jr.; 10. Problems in dynamical systems and related topics Boris Hasselblatt.