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A note on Poincaré recurrence for semigroup actions via Furstenberg family

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Abstract

This paper presents an explanation of recurrence for semigroup actions from two points of view. The first one considers the concept of recurrence in the Poincaré sense as stated in Souza (Semigroup Forum 83:351–370, 2011) while the second one considers the notion of recurrence via a Fursternberg family as defined in Akin (Recurrence in Topological Dynamics. Furstenberg and Ellis Action. Plenum Press, New York, 1997). A relationship between these notions of recurrence is presented.

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Acknowledgments

Research supported by Fundação Araucária Grant 476/14.

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Correspondence to Josiney A. Souza.

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Communicated by Jimmie D. Lawson.

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Tozatti, H.V.M., Souza, J.A. A note on Poincaré recurrence for semigroup actions via Furstenberg family. Semigroup Forum 94, 181–188 (2017). https://doi.org/10.1007/s00233-016-9828-3

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  • DOI: https://doi.org/10.1007/s00233-016-9828-3

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