Dynamics, Ergodic Theory and Geometry
Cambridge University Press, Sep 24, 2007 - Mathematics - 324 pages
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.
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algebraic Anosov diffeomorphisms Anosov ﬂows attractors automorphisms billiard 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 ﬁeld ﬁnite ﬁrst ﬁxed points foliations geodesic ﬂow Gibbs measure Gromov group actions group G Hamiltonian Hausdorff Hofer holonomies homomorphism hyperbolic diffeomorphisms hyperbolic sets inﬁnite integer invariant measure leaf segments Lemma locally rigid Margulis Markov rectangle Math metric model set Op2n orbit partially hyperbolic parties finies periodic perturbation project scheme proof random billiard reﬂection result Riemannian satisﬁes Section semisimple Lie group sequence smooth solenoid solenoid functions space spectrum stable and unstable structure subgroup subset sufﬁciently superrigidity surface symplectic capacities symplectic embedding symplectic geometry symplectic manifolds Theorem tile set topological entropy topologically regular torus valid tiling Wang tiles