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Finitely represented closed-orbit subdynamics for commuting automorphisms

Published online by Cambridge University Press:  13 October 2009

RICHARD MILES
RICHARD MILES*
Affiliation:
Department of Mathematics, KTH, SE-100 44 Stockholm, Sweden (email: ricmiles@math.kth.se)
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Abstract

The purpose of this paper is to exhibit highly structured subdynamics for a class of non-expansive algebraic ℤd-actions based on the closed orbits of elements of an action. This is done using dynamical Dirichlet series to encode orbit counts. It is shown that there is a distinguished group homomorphism from ℤd onto a finite abelian group that controls the form of the Dirichlet series of elements of an action and that these series have common analytic properties. Corresponding orbit growth asymptotics are subsequently investigated.

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Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 30 , Issue 6 , December 2010 , pp. 1787 - 1802
Copyright
Copyright © Cambridge University Press 2009

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