Taiwanese Journal of Mathematics

Devaney's Chaos for Maps on $G$-spaces

Ekta Shah

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Abstract

We study the notion of sensitivity on $G$-spaces and through examples observe that $G$-sensitivity neither implies nor is implied by sensitivity. Further, we obtain necessary and sufficient conditions for a map to be $G$-sensitive. Next, we define the notion of Devaney's chaos on $G$-space and show that $G$-sensitivity is a redundant condition in the definition.

Article information

Source
Taiwanese J. Math., Volume 22, Number 2 (2018), 339-348.

Dates
Received: 25 February 2017
Revised: 9 June 2017
Accepted: 26 June 2017
First available in Project Euclid: 8 September 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1504836030

Digital Object Identifier
doi:10.11650/tjm/8168

Mathematical Reviews number (MathSciNet)
MR3780721

Zentralblatt MATH identifier
06965374

Subjects
Primary: 37D05: Hyperbolic orbits and sets 37B20: Notions of recurrence 37C85: Dynamics of group actions other than Z and R, and foliations [See mainly 22Fxx, and also 57R30, 57Sxx] 54H20: Topological dynamics [See also 28Dxx, 37Bxx]

Keywords
transitive maps sensitive dependence on initial conditions Devaney's chaos metric $G$-space

Citation

Shah, Ekta. Devaney's Chaos for Maps on $G$-spaces. Taiwanese J. Math. 22 (2018), no. 2, 339--348. doi:10.11650/tjm/8168. https://projecteuclid.org/euclid.twjm/1504836030


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