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.
Zamani Bahabadi, A. R., Effati, M., & Honary, B. (2021). Some remarks on chaos in nonautonomous dynamical systems. Khayyam Journal of Mathematics, 7(1), 115-130. doi: 10.22034/kjm.2020.209183.1631
MLA
Ali Reza Zamani Bahabadi; Mona Effati; Bahman Honary. "Some remarks on chaos in nonautonomous dynamical systems". Khayyam Journal of Mathematics, 7, 1, 2021, 115-130. doi: 10.22034/kjm.2020.209183.1631
HARVARD
Zamani Bahabadi, A. R., Effati, M., Honary, B. (2021). 'Some remarks on chaos in nonautonomous dynamical systems', Khayyam Journal of Mathematics, 7(1), pp. 115-130. doi: 10.22034/kjm.2020.209183.1631
VANCOUVER
Zamani Bahabadi, A. R., Effati, M., Honary, B. Some remarks on chaos in nonautonomous dynamical systems. Khayyam Journal of Mathematics, 2021; 7(1): 115-130. doi: 10.22034/kjm.2020.209183.1631
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