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ON HIGHER ORDER IRREGULAR SETS

Min Wu|Jinjun Li
대한수학회 (The Korean Mathematical Society)|2017.01|대한수학회지 (Journal of the KMS)|제54권 제1호|pp. 87-99

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참고문헌

키워드

residualhigher order irregular sethigher order maximal Birkhoff average oscillation
주제분류수학

초록

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.

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.

참고문헌 (27)

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