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H G BOTHB Berlin
A BUNIMOVICH Moscov
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abelian absolutely continuous amenable attractor automorphisms Banach space Borel sets Cantor set central limit theorem compact configuration spaces consider convergence countable countable group defined definition denote density diffeomorphisms dynamical system eigenvalues endomorphism entropy equation ergodic action ergodic automorphism ergodic equivalence relation example exists expanding attractors finite dimensional finite measure preserving fractal function f given group actions Hausdorff dimension hyperfinite integrable interval invariant measures isomorphism Lebesgue measure Lemma lim sup manifold maps Markov chains Markov operator martingale Math Mathematics measure space metric Morse sequence natural number Neumann algebras nonexpansive nonsingular automorphisms obtain orbit equivalence order preserving periodic orbit positive Preprint probability measure probability space probability space X,S,u problem product type proof Proposition prove Random ergodic theorem real numbers satisfying Sektion Mathematik semigroups spectral spectrum stochastic strongly ergodic subset theory topological transformations transverse Hausdorff dimension unstable manifold weakly mixing zero