Dynamics, Ergodic Theory and GeometryBoris Hasselblatt 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. |
Contents
Section 1 | 45 |
Section 2 | 99 |
Section 3 | 113 |
Section 4 | 129 |
Section 5 | 145 |
Section 6 | 161 |
Section 7 | 165 |
Section 8 | 171 |
Section 9 | 172 |
Section 10 | 179 |
Section 11 | 196 |
Section 12 | 205 |
Section 13 | 220 |
Section 14 | 223 |
Section 15 | 243 |
Section 16 | 273 |
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Common terms and phrases
affine algebraic Anosov diffeomorphisms Anosov flows attractors automorphisms billiard cell boundary cocompact lattice cocycle cohomology colors conjecture conjugacy conjugate construction cut and project defined definition denote dense dimension discrete dynamical systems Ekeland-Hofer capacities ellipsoids Ergodic Theory Ergodic Theory Dynam example exists finite foliations geodesic flows geometry Gibbs measure Gromov group actions group G Hamiltonian Hausdorff Hofer Hölder continuous holonomies homomorphism hyperbolic diffeomorphisms integer invariant measure leaf segments Lemma locally rigid Margulis Markov rectangle Math Mathematical metric model set orbit partially hyperbolic parties finies periodic perturbation project scheme proof random billiard result Riemannian Section semisimple Lie group sequence smooth solenoid functions space spectrum stable and unstable structure subgroup subset superrigidity surface symplectic capacities symplectic embeddings symplectic manifolds Theorem tile set topological entropy topologically regular torus valid tiling Wang tiles