Topological Dynamics and Applications: A Volume in Honor of Robert Ellis : Proceedings of a Conference in Honor of the Retirement of Robert Ellis, April 5-6, 1995, University of Minnesota
This book is a very readable exposition of the modern theory of topological dynamics and presents diverse applications to such areas as ergodic theory, combinatorial number theory and differential equations. There are three parts: 1) The abstract theory of topological dynamics is discussed, including a comprehensive survey by Furstenberg and Glasner on the work and influence of R. Ellis. Presented in book form for the first time are new topics in the theory of dynamical systems, such as weak almost-periodicity, hidden eigenvalues, a natural family of factors and topological analogues of ergodic decomposition. 2) The power of abstract techniques is demonstrated by giving a very wide range of applications to areas of ergodic theory, combinatorial number theory, random walks on groups and others. 3) Applications to non-autonomous linear differential equations are shown. Exposition on recent results about Floquet theory, bifurcation theory and Lyapanov exponents is given.
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abelian action algebra amenable groups Amer assume automorphic Borel cascade closed cocycle commutative condition converges COROLLARY countable covering cocycle defined DEFINITION denote dense differential equations distal eigenvalues element Ellis group entropy enveloping semigroup equicontinuous equicontinuous factor equivalence relation ergodic measures ergodic sheets ergodic theory example exists extension family of factors finite Furstenberg g e G G-flow Glasner group extension group G Hausdorff hence homomorphism idempotent implies invariant measure invariant subset isometric isomorphism LEMMA linear Lyapunov exponent Math Mathematics Subject Classification metric space minimal set minimal subset natural family periodic proacimal PROOF PROPOSITION prove proximal result satisfying Section semigroup sequence set of chromatic set of measurable set of topological solution syndetic T-closed subgroup Theorem topological dynamics topological group Trans transformation transitive weakly mixing