Periodic measures are dense in invariant measures for residually finite amenable group actions with specification

Xiankun Ren

doi:10.3934/dcds.2018068

Article Contents

2018, Volume 38, Issue 4: 1657-1667. Doi: 10.3934/dcds.2018068

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Periodic measures are dense in invariant measures for residually finite amenable group actions with specification

Xiankun Ren^1,2,

1.
School of Mathematical Sciences, Peking University, Beijing 100871, China
2.
Department of Mathematics, SUNY at Buffalo, Buffalo, NY 14260-2900, USA

Received: December 31, 2015

Revised: September 30, 2017

Published: June 2018

The author is supported by NNSFC grant No.11471344.

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Abstract

We prove that for actions of a discrete countable residuallyfinite amenable group on a compact metric space with specification property, periodic measures are dense in theset of invariant measures. We also prove that certain expansiveactions of a countable discrete group by automorphisms of compact abelian groups have specification property.

Keywords:

Residually finite amenable group action,
periodic measure,
specification property.

Mathematics Subject Classification: Primary: 37B40, 37A35, 22D25.

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References

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