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On almost specification and average shadowing properties

Volume 224 / 2014

Marcin Kulczycki, Dominik Kwietniak, Piotr Oprocha Fundamenta Mathematicae 224 (2014), 241-278 MSC: Primary 37B05; Secondary 34D05, 37D45. DOI: 10.4064/fm224-3-4

Abstract

We study relations between the almost specification property, the asymptotic average shadowing property and the average shadowing property for dynamical systems on compact metric spaces. We show implications between these properties and relate them to other important notions such as shadowing, transitivity, invariant measures, etc. We provide examples showing that compactness is a necessary condition for these implications to hold. As a consequence, we also obtain a proof that limit shadowing in chain transitive systems implies shadowing.

Authors

  • Marcin KulczyckiFaculty of Mathematics and
    Computer Science
    Jagiellonian University
    Łojasiewicza 6
    30-348 Kraków, Poland
    e-mail
  • Dominik KwietniakFaculty of Mathematics and
    Computer Science
    Jagiellonian University
    Łojasiewicza 6
    30-348 Kraków, Poland
    e-mail
  • Piotr OprochaAGH University of Science and Technology
    Faculty of Applied Mathematics
    Al. A. Mickiewicza 30
    30-059 Kraków, Poland
    and
    Institute of Mathematics
    Polish Academy of Sciences
    Śniadeckich 8
    00-956 Warszawa, Poland
    e-mail

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