On the Large Deviations Theorem of Weaker Types

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalNot applicablepeer-review

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Detail(s)

Original languageEnglish
Article number1750127
Journal / PublicationInternational Journal of Bifurcation and Chaos
Volume27
Issue number8
Publication statusPublished - Jul 2017

Abstract

In this paper, we introduce the concepts of the large deviations theorem of weaker types, i.e. type I, type I’, type II, type II’, type III, and type III’, and present a systematic study of the ergodic and chaotic properties of dynamical systems satisfying the large deviations theorem of various types. Some characteristics of the ergodic measure are obtained and then applied to prove that every dynamical system satisfying the large deviations theorem of type I’ is ergodic, which is equivalent to the large deviations theorem of type II’ in this regard, and that every uniquely ergodic dynamical system restricted on its support satisfies the large deviations theorem. Moreover, we prove that every dynamical system satisfying the large deviations theorem of type III is an E-system.

Research Area(s)

  • chaos, equicontinuous, ergodicity, Large deviations theorem, sensitivity, transitivity