Stronger Forms of Sensitivity in the Dynamical System of Abelian Semigroup Actions

In this paper, we continue the study of abelian semigroup actions of several stronger versions of sensitivity, such as syndetically sensitive, thickly sensitive and thickly syndetically sensitive. We derive some sufficient conditions for a dynamical system to have these sensitivities. Also, we prove...

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Bibliographic Details
Published inJournal of dynamical and control systems Vol. 28; no. 1; pp. 151 - 162
Main Authors Renukadevi, V., Tamilselvi, S.
Format Journal Article
LanguageEnglish
Published New York Springer US 2022
Springer Nature B.V
Subjects
Calculus of Variations and Optimal Control; Optimization
Control
Dynamical Systems
Dynamical Systems and Ergodic Theory
Mathematics
Mathematics and Statistics
Semigroups
Sensitivity
Systems Theory
Vibration
Thickly syndetically sensitive
Semigroup action
Primary: 54H20
Syndetically sensitive
54E15
Weakly mixing
Thickly sensitive
37B05
16W22
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Summary:In this paper, we continue the study of abelian semigroup actions of several stronger versions of sensitivity, such as syndetically sensitive, thickly sensitive and thickly syndetically sensitive. We derive some sufficient conditions for a dynamical system to have these sensitivities. Also, we prove that the minimal and sensitive system is syndetically sensitive and non-minimal M -system is thickly syndetically sensitive. Some other significant properties of this new class are obtained.
ISSN:1079-2724
1573-8698
DOI:10.1007/s10883-020-09527-w