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Periodic Points of Regular Curve Homeomorphisms

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Abstract

We prove that, if \(f:X\rightarrow X\) is a regular curve homeomorphism then the set of periodic points is either empty or dense in the set of non-wandering points. Moreover, we prove that each infinite minimal set is approximated by periodic orbits and is conjugate to an adding machine when the set of periodic points is not empty. Furthermore, we give a characterization of equicontinuous regular curve homeomorphisms

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Acknowledgements

The authors are thankful to the referees for their careful reading of the manuscript, helpful remarks and suggestions which improve the presentation of the paper.

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Authors and Affiliations

  1. University of Carthage, faculty of sciences of bizerte (UR17ES21), “Dynamical Systems and their Applications”, 7021, Jarzouna, Tunisia

    Aymen Daghar, Issam Naghmouchi & Moncef Riahi

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  1. Aymen Daghar
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  2. Issam Naghmouchi
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  3. Moncef Riahi
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Correspondence to Issam Naghmouchi.

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Daghar, A., Naghmouchi, I. & Riahi, M. Periodic Points of Regular Curve Homeomorphisms. Qual. Theory Dyn. Syst. 20, 32 (2021). https://doi.org/10.1007/s12346-021-00471-z

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  • DOI: https://doi.org/10.1007/s12346-021-00471-z

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