A dichotomy in orbit growth for commuting automorphisms

Richard Miles; Thomas Ward

doi:10.1112/jlms/jdq010

A dichotomy in orbit growth for commuting automorphisms

Richard Miles, Thomas Ward

School of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

We consider asymptotic orbit-counting problems for certain expansive actions by commuting automorphisms of compact groups. A dichotomy is found between systems with asymptotically more periodic orbits than the topological entropy predicts, and those for which there is no excess of periodic orbits.

Original language	English
Pages (from-to)	715-726
Number of pages	12
Journal	Journal of the London Mathematical Society
Volume	81
Issue number	3
DOIs	https://doi.org/10.1112/jlms/jdq010
Publication status	Published - 2010

Access to Document

10.1112/jlms/jdq010

http://arxiv.org/abs/0904.3492

Cite this

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title = "A dichotomy in orbit growth for commuting automorphisms",

abstract = "We consider asymptotic orbit-counting problems for certain expansive actions by commuting automorphisms of compact groups. A dichotomy is found between systems with asymptotically more periodic orbits than the topological entropy predicts, and those for which there is no excess of periodic orbits.",

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AB - We consider asymptotic orbit-counting problems for certain expansive actions by commuting automorphisms of compact groups. A dichotomy is found between systems with asymptotically more periodic orbits than the topological entropy predicts, and those for which there is no excess of periodic orbits.

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DO - 10.1112/jlms/jdq010

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EP - 726

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

SN - 0024-6107

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