Uniform periodic point growth in entropy rank one
نویسندگان
چکیده
منابع مشابه
Uniform Periodic Point Growth in Entropy Rank One
We show that algebraic dynamical systems with entropy rank one have uniformly exponentially many periodic points in all directions.
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We show that algebraic dynamical systems with entropy rank one have uniformly exponentially many periodic points in all directions.
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A framework for understanding the geometry of continuous actions of Z was developed by Boyle and Lind using the notion of expansive behavior along lower-dimensional subspaces. For algebraic Z-actions of entropy rank one, the expansive subdynamics is readily described in terms of Lyapunov exponents. Here we show that periodic point counts for elements of an entropy rank one action determine the ...
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A framework for understanding the geometry of continuous actions of Z was developed by Boyle and Lind using the notion of expansive behavior along lower-dimensional subspaces. For algebraic Z-actions of entropy rank one, the expansive subdynamics is readily described in terms of Lyapunov exponents. Here we show that periodic point counts for elements of an entropy rank one action determine the ...
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Rank one transformations play a central role in the theory of ergodic measure preserving transformations. Having first been identified as a distinct class by Chacon in [3], their properties have been studied extensively (see for example [1], [7], [11], [6]). Rank one transformations have also served as an important tool for exploring the range of possible behavior of measure preserving transfor...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2008
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-07-09018-1