The dynamics of nonautonomous dynamical systems with the large deviations theorem. Issue 3 (3rd July 2021)

• Record Type: Journal Article
• Authors: Tang, Yanjie; Yin, Jiandong
• Is Part Of: Dynamical systems. Volume 36:Issue 3(2021)
• Page Start: 416
• Page End: 426
• Publication Date: 2021-07-03
• Subjects: Large deviations theorem -- topological ergodicity -- ergodic sensitivity -- measure expansiveness; 54H20 -- 37D45; Differentiable dynamical systems -- Periodicals; 515.35205
• DOI: 10.1080/14689367.2021.1926430
• Languages: English
• ISSNs: 1468-9367

Abstract

Abstract : Let ( X, F ) be a nonautonomous dynamical system and μ be a Borel measure on X with a full support. The purpose of this paper is to introduce the concepts of large deviations theorem and expansive measure for nonautonomous discrete systems and investigate the dynamics of nonautonomous dynamical systems with the large deviations theorem. Actually, it is proved that ( X, F ) is ergodicaly sensitive if the pair ( F, μ ) satisfies the large deviations theorem and ( X, F ) is topologically strongly ergodic; ( X, F ) is topologically ergodic if the pair ( F, μ ) satisfies the large deviations theorem in a sequence of positive integers; μ is expansive if the pair ( F, μ ) satisfies the large deviations theorem and ( X, F ) is topologically strongly ergodic and each measurable set with positive measure with respect to μ has a nonempty interior.