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Recurrence Theorem for Semigroup Actions

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Abstract

In this article the notion of Poincaré recurrence for semigroup actions is introduced. It recovers the well-known concept of recurrence in dynamical systems. The Poincaré recurrence theorem is extended from the setting of flows on metric spaces to the setting of semigroup actions on metric spaces. The results are applied to control systems and semigroups acting on fiber bundles.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Estadual de Maringá, Cx. Postal 331, 87.020-900, Maringá, PR, Brazil

    Josiney A. Souza

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  1. Josiney A. Souza
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Correspondence to Josiney A. Souza.

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Communicated by Jimmie D. Lawson.

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Souza, J.A. Recurrence Theorem for Semigroup Actions. Semigroup Forum 83, 351–370 (2011). https://doi.org/10.1007/s00233-011-9334-6

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  • DOI: https://doi.org/10.1007/s00233-011-9334-6

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