# American Institute of Mathematical Sciences

February  2014, 34(2): 635-645. doi: 10.3934/dcds.2014.34.635

## Generic property of irregular sets in systems satisfying the specification property

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

Received  May 2013 Revised  June 2013 Published  August 2013

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.
Citation: Jinjun Li, Min Wu. Generic property of irregular sets in systems satisfying the specification property. Discrete & Continuous Dynamical Systems - A, 2014, 34 (2) : 635-645. doi: 10.3934/dcds.2014.34.635
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##### References:
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