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  • Cited by 5
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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Ward, Thomas and Miles, Richard 2015. Directional uniformities, periodic points, and entropy. Discrete and Continuous Dynamical Systems - Series B, Vol. 20, Issue. 10, p. 3525.


    Bell, Jason Miles, Richard and Ward, Thomas 2014. Towards a Pólya–Carlson dichotomy for algebraic dynamics. Indagationes Mathematicae, Vol. 25, Issue. 4, p. 652.


    Ward, Thomas and Miles, Richard 2011. A directional uniformity of periodic point distribution and mixing. Discrete and Continuous Dynamical Systems, Vol. 30, Issue. 4, p. 1181.


    Baake, Michael Lau, Eike and Paskunas, Vytautas 2010. A note on the dynamical zeta function of general toral endomorphisms. Monatshefte für Mathematik, Vol. 161, Issue. 1, p. 33.


    MILES, RICHARD 2010. Finitely represented closed-orbit subdynamics for commuting automorphisms. Ergodic Theory and Dynamical Systems, Vol. 30, Issue. 06, p. 1787.


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Zeta functions for elements of entropy rank-one actions

  • RICHARD MILES (a1)
  • DOI: http://dx.doi.org/10.1017/S0143385706000794
  • Published online: 12 February 2007
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.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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