## Proceedings of the Conference Ergodic Theory and Related Topics II, Georgenthal (Thuringia), GDR, April 20-25, 1986, Volume 2 |

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abelian absolutely continuous amenable attractors automorphisms Banach space Borel sets called central limit theorem compact configuration spaces consider convergence countable countable group defined definition denote density dynamical systems eigenvalues endomorphism entropy equation ergodic action ergodic automorphism ergodic equivalence relation example exists expanding attractor finite dimensional finite measure preserving fractal free path function f given Hausdorff dimension Hence Hilbert space integrable interval invariant measures isomorphic Lebesgue measure Lemma lim sup Lorentz gas manifold Markov chains Markov operator Math Mathematics measure space Morse sequence natural number nonexpansive nonsingular automorphisms o-algebra obtain one-dimensional orbit equivalence order preserving particle periodic orbit positive Preprint probability measure probability space probability space X,S,u problem product type proof Proposition prove Random ergodic theorem real numbers respect satisfying semigroup spectral spectrum stochastic strongly ergodic subset supp(a theory topological transverse Hausdorff dimensions unstable manifolds weakly mixing zero