Some remarks on chaos in nonautonomous dynamical systems

Document Type : Original Article

Authors

Ali Reza Zamani Bahabadi ¹

Mona Effati ²

Bahman Honary ³

¹ Ferdowsi University of Mashhad

² Pure Mathematics, Faculty of Mathematical science, Mashhad, Iran

³ Ferdowsi university of Mashhhad

10.22034/kjm.2020.209183.1631

Abstract

‎‎We introduce the concept of almost thick chaos and continuously almost thick transitivity for continuous maps and nonautonomous dynamical systems (NDS)‎. ‎We show that NDS $f_{1,\infty}$ is sensitive if it is thick transitive and syndetic‎.
‎Under certain conditions‎, ‎we show that NDS $(X,f_{1,\infty})$ generated by a sequence $(f_n)$ of continuous maps on $X$ converging uniformly to $f$ is almost thick transitive if and only if $(X,f)$ is almost thick transitive‎.
‎Moreover‎, ‎we prove that if $f_{1,\infty}$ is continuously almost thick transitive and syndetic‎, ‎then it is strongly topologically ergodic‎. ‎In addition‎, ‎the relationship between the large deviations theorem and almost thick chaos is studied‎.

Keywords

Nonautonomous dynamical systems

Transitivity

Sen- sitivity

Chaos

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