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Lyapunov Stability and Attraction Under Equivariant Maps

Published online by Cambridge University Press:  20 November 2018

Carlos Braga Barros ,
Victor Rocha  and
Josiney Souza
Carlos Braga Barros
Affiliation:
Departamento de Matemática, Universidade Estadual de Maringá, Maringá-PR Brasil 87020-900. e-mail: cjbbarros@uem.br, victor.hlr@hotmail.com, jasouza3@uem.br
Victor Rocha
Affiliation:
Departamento de Matemática, Universidade Estadual de Maringá, Maringá-PR Brasil 87020-900. e-mail: cjbbarros@uem.br, victor.hlr@hotmail.com, jasouza3@uem.br
Josiney Souza
Affiliation:
Departamento de Matemática, Universidade Estadual de Maringá, Maringá-PR Brasil 87020-900. e-mail: cjbbarros@uem.br, victor.hlr@hotmail.com, jasouza3@uem.br
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Abstract

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Let $M$ and $N$ be admissible Hausdorff topological spaces endowed with admissible families of open coverings. Assume that $\mathcal{S}$ is a semigroup acting on both $M$ and $N$. In this paper we study the behavior of limit sets, prolongations, prolongational limit sets, attracting sets, attractors, and Lyapunov stable sets (all concepts defined for the action of the semigroup $\mathcal{S}$) under equivariant maps and semiconjugations from $M$ to $N$.

Keywords

37B2537C7534C2734D05Lyapunov stabilitysemigroup actionsgeneralized flowsequivariant mapsadmissible topological spaces
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 67 , Issue 6 , 01 December 2015 , pp. 1247 - 1269
Copyright
Copyright © Canadian Mathematical Society 2015

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