Mixing transformations on metric spaces |
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| Authors: | T. Erber B. Schweizer A. Sklar |
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| Affiliation: | (1) Department of Physics, Illinois Institute of Technology, Chicago, Illinois, USA;(2) Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts, USA;(3) Department of Mathematics, Illinois Institute of Technology, Chicago, Illinois, USA |
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| Abstract: | It is proved that if a metric space is subjected to a mixing transformation, then there exists a positive numberx0 such that the probability that any arbitrary set of positive measure is asymptotically mapped into a set of diameter less thanx0 is zero. Physical implications of this result, in particular the interpretation of Poincaré recurrence, are discussed. |
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