%0 Journal Article
%T Some remarks on chaos in nonautonomous dynamical systems
%J Khayyam Journal of Mathematics
%I Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)
%Z 2423-4788
%A Zamani Bahabadi, Ali Reza
%A Effati, Mona
%A Honary, Bahman
%D 2021
%\ 01/01/2021
%V 7
%N 1
%P 115-130
%! Some remarks on chaos in nonautonomous dynamical systems
%K Nonautonomous dynamical systems
%K Transitivity
%K Sen- sitivity
%K chaos
%R 10.22034/kjm.2020.209183.1631
%X 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.
%U http://www.kjm-math.org/article_123056_08214b4428e55ce385d320df099089aa.pdf