TY - JOUR
ID - 123056
TI - Some remarks on chaos in nonautonomous dynamical systems
JO - Khayyam Journal of Mathematics
JA - KJM
LA - en
SN -
AU - Zamani Bahabadi, Ali Reza
AU - Effati, Mona
AU - Honary, Bahman
AD - Ferdowsi University of Mashhad
AD - Pure Mathematics, Faculty of Mathematical science, Mashhad, Iran
AD - Ferdowsi university of Mashhhad
Y1 - 2021
PY - 2021
VL - 7
IS - 1
SP - 115
EP - 130
KW - Nonautonomous dynamical systems
KW - Transitivity
KW - Sen- sitivity
KW - chaos
DO - 10.22034/kjm.2020.209183.1631
N2 - 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.
UR - https://www.kjm-math.org/article_123056.html
L1 - https://www.kjm-math.org/article_123056_08214b4428e55ce385d320df099089aa.pdf
ER -