Generic property of irregular sets in systems satisfying the specification property

Jinjun Li; Min Wu

doi:10.3934/dcds.2014.34.635

Article Contents

2014, Volume 34, Issue 2: 635-645. Doi: 10.3934/dcds.2014.34.635

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Generic property of irregular sets in systems satisfying the specification property

Jinjun Li^1, and
Min Wu^2,

1.
School of Mathematics and statistics, Minnan Normal University, Zhangzhou, 363000
2.
Department of Mathematics, South China University of Technology, Guangzhou, 510641

Received: April 30, 2013

Revised: May 31, 2013

Published: January 2014

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Abstract

Let $f$ be a continuous map on a compact metric space. In this paper, under the hypothesis that $f$ satisfies the specification property, we prove that the set consisting of those points for which the Birkhoff ergodic average does not exist is either residual or empty.

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Mathematics Subject Classification: Primary: 54H20; Secondary: 54E52.

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