منابع مشابه
Amenable Actions and Almost Invariant Sets
In this paper, we study the connections between properties of the action of a countable group Γ on a countable set X and the ergodic theoretic properties of the corresponding generalized Bernoulli shift, i.e., the corresponding shift action of Γ on MX , where M is a measure space. In particular, we show that the action of Γ on X is amenable iff the shift Γ ↪→MX has almost invariant sets.
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Let S be a topological semigroup acting on a topological space X. We develop the theory of (weakly) almost periodic functions on X, with respect to S, and form the (weakly) almost periodic compactifications of X and S, with respect to each other. We then consider the notion of an action of Son a Banach space, and on its dual, and after defining S-invariant means for such a space, we give a...
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We show that topological amenability of an action of a countable discrete group on a compact space is equivalent to the existence of an invariant mean for the action. We prove also that this is equivalent to vanishing of bounded cohomology for a class of Banach G-modules associated to the action, as well as to vanishing of a specific cohomology class. In the case when the compact space is a poi...
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Chaotic dynamical systems are often transitive, although this transitivity is sometimes very weak. It is of interest to divide the phase space into large regions, between which there is relatively little communication of trajectories. We present fast, simple algorithms to find such divisions. The present work builds on the results of Froyland and Dellnitz [G. Froyland, M. Dellnitz, Detecting an...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2007
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-07-09116-2