Uniform Periodic Point Growth in Entropy Rank One
نویسندگان
چکیده
We show that algebraic dynamical systems with entropy rank one have uniformly exponentially many periodic points in all directions.
منابع مشابه
Se p 20 06 UNIFORM PERIODIC POINT GROWTH IN ENTROPY RANK ONE RICHARD
We show that algebraic dynamical systems with entropy rank one have uniformly exponentially many periodic points in all directions.
متن کاملZeta Functions for Elements of Entropy Rank One Actions
An algebraic Z-action of entropy rank one is one for which each element has finite entropy. Using the structure theory of these actions due to Einsiedler and Lind, this paper investigates dynamical zeta functions for elements of the action. An explicit periodic point formula is obtained leading to a uniform parameterization of the zeta functions that arise in expansive components of an expansiv...
متن کاملPeriodic 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 کاملA Directional Uniformity of Periodic Point Distribution and Mixing
For mixing Zd-actions generated by commuting automorphisms of a compact abelian group, we investigate the directional uniformity of the rate of periodic point distribution and mixing. When each of these automorphisms has finite entropy, it is shown that directional mixing and directional convergence of the uniform measure supported on periodic points to Haar measure occurs at a uniform rate ind...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006