Sensitivity of non-autonomous discrete dynamical systems revisited

Ding, Xian-Feng ¹ ; Lu, Tian-Xiu ² ; Wang, Jian-Jun ³

¹ School of Sciences, Southwest Petroleum University, Chengdu, Sichuan, 610500, People’s Republic of China
² School of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong, Sichuan, 643000, People’s Republic of China
³ Department of Applied Mathematics, Sichuan Agricultural University, Ya’an, Sichuan, 625014, People’s Republic of China

Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 10, p. 5239-5244.

Résumé

In this note, we construct a transitive non-autonomous discrete system with strongly periodic density which is not sensitive. Besides, we prove that every transitive non-autonomous discrete system with almost periodic density is syndetically sensitive, provided that it converges uniformly to a map, and that a product system is multi-sensitive (resp., $\mathcal{F}$-sensitive) if and only if there exists a factor system is multi-sensitive (resp., $\mathcal{F}$-sensitive), where $\mathcal{F}$ is a filterdual.

Détail

DOI : 10.22436/jnsa.010.10.10

Classification : 37B55, 54H20
Keywords: \(\mathcal{F}\)-sensitivity, Non-autonomous discrete system \(({\bf NADS})\), sensitivity, transitivity, product system

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