On stronger forms of sensitivity in non-autonomous systems
type: Item
instance of: scholarly article
title: On stronger forms of sensitivity in non-autonomous systems
zbMATH Open document ID: 1403.54024
author: Radhika Vasisht
author: Ruchi Das
published in: Taiwanese Journal of Mathematics
publication date: 2018-10-25T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.twjm/1524708018
review text: In this paper, some stronger forms of transitivity are discussed for non-autonomous discrete dynamical systems (NDS). The following is the main result: Theorem. Let \((X,f_{1,\infty})\) be an NDS generated by a family \(f_{1,\infty}\) of feeble open maps commuting with \(f\) and fulfilling \(\sum_i D(f_i,f)< \infty\). Then i) \((X,f)\) is syndetically transitive iff \((X,f_{1,\infty})\) is syndetically transitive ii) \((X,f)\) is topologically ergodic iff \((X,f_{1,\infty})\) is topologically ergodic iii) \((X,f)\) is syndetically sensitive iff \((X,f_{1,\infty})\) is syndetically sensitive iv) \((X,f)\) is thickly sensitive iff \((X,f_{1,\infty})\) is thickly sensitive v) \((X,f)\) is thickly syndetic sensitive iff \((X,f_{1,\infty})\) is thickly syndetic sensitive vi) \((X,f)\) is ergodically sensitive iff \((X,f_{1,\infty})\) is ergodically sensitive vii) \((X,f)\) is multi-sensitive iff \((X,f_{1,\infty})\) is multi-sensitive. Further aspects occasioned by these developments are also discussed.
Mathematics Subject Classification ID: 54H20
Mathematics Subject Classification ID: 37B55
zbMATH DE Number: 6965413
zbMATH Keywords: non-autonomous dynamical system
zbMATH Keywords: thick/ergodic/multi sensitivity
zbMATH Keywords: transitive property
reviewed by: Mihai Turinici
MaRDI profile type: Publication
OpenAlex ID: W2799659432
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DOI: 10.11650/TJM/180406
description: scientific article; zbMATH DE number 6965413