Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-29T01:58:19.942Z Has data issue: false hasContentIssue false
  • English
  • Français

Zeta functions for elements of entropy rank-one actions

Published online by Cambridge University Press:  12 February 2007

RICHARD MILES
RICHARD MILES
Affiliation:
School of Mathematics, University of East Anglia, Norwich NR4 7TJ, UK (e-mail: [email protected])
Get access Rights & Permissions [Opens in a new window]

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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 27 , Issue 2 , April 2007 , pp. 567 - 582
Copyright
2007 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)