Taiwanese Journal of Mathematics

On Stronger Forms of Sensitivity in Non-autonomous Systems

Radhika Vasisht and Ruchi Das

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Abstract

In this paper, some stronger forms of transitivity in a non-autonomous discrete dynamical system $(X,f_{1,\infty})$ generated by a sequence $(f_n)$ of continuous self maps converging uniformly to $f$, are studied. The concepts of thick sensitivity, ergodic sensitivity and multi-sensitivity for non-autonomous discrete dynamical systems, which are all stronger forms of sensitivity, are defined and studied. It is proved that under certain conditions, if the rate of convergence at which $(f_n)$ converges to $f$ is “sufficiently fast”, then various forms of sensitivity and transitivity for the non-autonomous system $(X,f_{1,\infty})$ and the autonomous system $(X,f)$ coincide. Also counter examples are given to support results.

Article information

Source
Taiwanese J. Math., Volume 22, Number 5 (2018), 1139-1159.

Dates
Received: 15 December 2017
Revised: 6 April 2018
Accepted: 23 April 2018
First available in Project Euclid: 26 April 2018

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1524708018

Digital Object Identifier
doi:10.11650/tjm/180406

Mathematical Reviews number (MathSciNet)
MR3859370

Zentralblatt MATH identifier
06965413

Subjects
Primary: 54H20: Topological dynamics [See also 28Dxx, 37Bxx]
Secondary: 37B55: Nonautonomous dynamical systems

Keywords
non-autonomous dynamical systems sensitivity transitivity

Citation

Vasisht, Radhika; Das, Ruchi. On Stronger Forms of Sensitivity in Non-autonomous Systems. Taiwanese J. Math. 22 (2018), no. 5, 1139--1159. doi:10.11650/tjm/180406. https://projecteuclid.org/euclid.twjm/1524708018


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