Lyapunov Stability and Attraction Under Equivariant Maps

Barros, Carlos Braga ; Rocha, Victor ; Souza, Josiney

Canadian journal of mathematics, Tome 67 (2015) no. 6, pp. 1247-1269

Résumé

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 $N$ .

Détail

DOI : 10.4153/CJM-2015-007-7

Mots-clés : 37B25, 37C75, 34C27, 34D05, Lyapunov stability, semigroup actions, generalized flows, equivariant maps, admissible topological spaces

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