@article {
author = {Zamani Bahabadi, Ali Reza and Effati, Mona and Honary, Bahman},
title = {Some remarks on chaos in nonautonomous dynamical systems},
journal = {Khayyam Journal of Mathematics},
volume = {7},
number = {1},
pages = {115-130},
year = {2021},
publisher = {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)},
issn = {2423-4788},
eissn = {2423-4788},
doi = {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},
url = {http://www.kjm-math.org/article_123056.html},
eprint = {http://www.kjm-math.org/article_123056_08214b4428e55ce385d320df099089aa.pdf}
}