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Lyapunov stability for semigroup actions

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Abstract

In this paper we introduce a theory of Lyapunov stability of sets for semigroup actions on Tychonoff spaces. We also present the main properties and the main results relating these new concepts. We generalize several concepts and results of Lyapunov stable sets from Bhatia and Hajek (Local Semi-Dynamical Systems. Lecture Notes in Mathematics, vol. 90. Springer, Berlin, 1969), Bhatia and Szegö (Dynamical Systems: Stability Theory and Applications. Lecture Notes in Mathematics, vol. 35. Springer, Berlin, 1967; and Stability Theory of Dynamical Systems. Springer, Berlin, 1970).

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Estadual de Maringá, Maringá, PR, 87020-900, Brasil

    Carlos J. Braga Barros, Josiney A. Souza & Victor H. L. Rocha

Authors
  1. Carlos J. Braga Barros
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  2. Josiney A. Souza
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  3. Victor H. L. Rocha
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Corresponding author

Correspondence to Carlos J. Braga Barros.

Additional information

Communicated by Jimmie D. Lawson.

Research supported by Fundação Araucária conv. 993/12 prot. 24906 and CNPq 476024/2012-9 Universal 14/2012.

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Braga Barros, C.J., Souza, J.A. & Rocha, V.H.L. Lyapunov stability for semigroup actions. Semigroup Forum 88, 227–249 (2014). https://doi.org/10.1007/s00233-013-9527-2

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  • DOI: https://doi.org/10.1007/s00233-013-9527-2

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