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Positively N-expansive Homeomorphisms and the L-shadowing Property

  • Bernardo CarvalhoEmail author
  • Welington Cordeiro
Article
  • 43 Downloads

Abstract

We discuss further the dynamics of n-expansive homeomorphisms with the shadowing property, started in Carvalho and Cordeiro (J Differ Equ 261:3734–3755, 2016). The L-shadowing property is defined and the dynamics of n-expansive homeomorphisms with such property is explored. In particular, we prove that positively n-expansive homeomorphisms with the L-shadowing property can only be defined in finite metric spaces.

Keywords

Expansive n-expansive Shadowing Limit shadowing 

Mathematics Subject Classification

Primary 37B99 Secondary 37D99 

Notes

Acknowledgements

Part of this work was developed while the first author was working at UFV-Brazil and the second author was at IMPA being supported by CNPq(Brazil).

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Departamento de MatemáticaUniversidade Federal de Minas Gerais - UFMGBelo HorizonteBrazil
  2. 2.Institute of Mathematics, Polish Academy of SciencesWarszawaPoland

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