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1 results

Lyapunov Stability and Attraction Under Equivariant Maps
Carlos Braga Barros, Victor Rocha, Josiney Souza
Journal:

Canadian Journal of Mathematics / Volume 67 / Issue 6 / 01 December 2015

Published online by Cambridge University Press:

20 November 2018, pp. 1247-1269

Print publication:

01 December 2015
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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 $N$.