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.
Jinjun Li and Min Wu
Minnan Normal University, South China University of Technology
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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