Based on the subjects from the Clay Mathematics Institute/Mathematical Sciences Research Institute Workshop titled 'Recent Progress in Dynamics' in September and October 2004, this volume contains surveys and research articles by leading experts in several areas of dynamical systems that have experienced substantial progress. One of the major surveys is on symplectic geometry, which is closely related to classical mechanics and an exciting addition to modern geometry. The survey on local rigidity of group actions gives a broad and up-to-date account of another flourishing subject. Other papers cover hyperbolic, parabolic, and symbolic dynamics as well as ergodic theory. Students and researchers in dynamical systems, geometry, and related areas will find this book fascinating. The book also includes a fifty-page commented problem list that takes the reader beyond the areas covered by the surveys, to inspire and guide further research.

• Many open problems • Combination of survey and research reports

### Contents

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'Ornstein–Weiss d'après 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 Halmos–von Neumann theorem for model sets, and almost automorphic dynamical systems E. Arthur Robinson Jr.; 10. Problems in dynamical systems and related topics Boris Hasselblatt.