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ON HIGHER ORDER IRREGULAR SETS

  • Li, Jinjun (School of Mathematics and Statistics Minnan Normal University) ;
  • Wu, Min (Department of Mathematics South China University of Technology)
  • Received : 2015.10.03
  • Published : 2017.01.01

Abstract

To indicate the statistical complexity of dynamical systems, we introduce the notions of higher order irregular set and higher order maximal Birkhoff average oscillation in this paper. We prove that, in the setting of topologically mixing Markov chain, the set consisting of those points having maximal k-order Birkhoff average oscillation for all positive integers k is as large as the whole space from the topological point of view. As applications, we discuss the corresponding results on a repeller.

Keywords

higher order irregular set;higher order maximal Birkhoff average oscillation;residual

Acknowledgement

Supported by : National Natural Science Foundation of China

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