Periodic point data detects subdynamics in entropy rank one
نویسندگان
چکیده
منابع مشابه
Periodic Point Data Detects Subdynamics in Entropy Rank One
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 ...
متن کاملFe b 20 06 PERIODIC POINT DATA DETECTS SUBDYNAMICS IN ENTROPY RANK ONE
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 ...
متن کاملUniform 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.
متن کاملRANK ONE Zd ACTIONS AND DIRECTIONAL ENTROPY
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: Ergodic Theory and Dynamical Systems
سال: 2006
ISSN: 0143-3857,1469-4417
DOI: 10.1017/s014338570600054x