Zeta functions for elements of entropy rank one actions

MILES, Richard (2007). Zeta functions for elements of entropy rank one actions. Ergodic Theory and Dynamical Systems, 27 (2), 567-582.

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Abstract

An algebraic $\mathbb{Z}^d$-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 expansive action, together with necessary and sufficient conditions for rationality in a more general setting.

Item Type:	Article
Departments - Does NOT include content added after October 2018:	Faculty of Social Sciences and Humanities > Department of Teacher Education
Identification Number:	https://doi.org/10.1017/50143385706000794
Page Range:	567-582
Depositing User:	Richard Miles
Date Deposited:	26 Jan 2018 13:41
Last Modified:	18 Mar 2021 16:30
URI:	https://shura.shu.ac.uk/id/eprint/17236

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