@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)}, 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 = {https://www.kjm-math.org/article_123056.html}, eprint = {https://www.kjm-math.org/article_123056_08214b4428e55ce385d320df099089aa.pdf} }