Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2017; 54(1): 87-99

Online first article October 14, 2016      Printed January 1, 2017

https://doi.org/10.4134/JKMS.j150597

Copyright © The Korean Mathematical Society.

On higher order irregular sets

Jinjun Li and Min Wu

Minnan Normal University, South China University of Technology

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

MSC numbers: 37B10, 54E52, 37C45

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