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Lyapunov Stability and Attraction Under Equivariant Maps

  Published:2015-03-31
 Printed: Dec 2015
  • Carlos Braga Barros,
    Departamento de Matemática, Universidade Estadual de Maringá, Maringá-PR Brasil 87020-900
  • Victor Rocha,
    Departamento de Matemática, Universidade Estadual de Maringá, Maringá-PR Brasil 87020-900
  • Josiney Souza,
    Departamento de Matemática, Universidade Estadual de Maringá, Maringá-PR Brasil 87020-900
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Abstract

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: Lyapunov stability, semigroup actions, generalized flows, equivariant maps, admissible topological spaces Lyapunov stability, semigroup actions, generalized flows, equivariant maps, admissible topological spaces
MSC Classifications: 37B25, 37C75, 34C27, 34D05 show english descriptions Lyapunov functions and stability; attractors, repellers
Stability theory
Almost and pseudo-almost periodic solutions
Asymptotic properties
37B25 - Lyapunov functions and stability; attractors, repellers
37C75 - Stability theory
34C27 - Almost and pseudo-almost periodic solutions
34D05 - Asymptotic properties
 

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