Properties of dynamical systems with the asymptotic average shadowing property

Volume 212 / 2011

Marcin Kulczycki, Piotr Oprocha Fundamenta Mathematicae 212 (2011), 35-52 MSC: Primary 37B05; Secondary 34D05, 37D45. DOI: 10.4064/fm212-1-3

Abstract

This article investigates under what conditions nontransitivity can coexist with the asymptotic average shadowing property. We show that there is a large class of maps satisfying both conditions simultaneously and that it is possible to find such examples even among maps on a compact interval. We also study the limit shadowing property and its relation to the asymptotic average shadowing property.

Authors

  • Marcin KulczyckiInstitute of Mathematics
    Jagiellonian University
    Łojasiewicza 6
    30-348 Kraków, Poland
    e-mail
  • Piotr OprochaDepartamento de Matemáticas
    Universidad de Murcia
    Campus de Espinardo
    30100 Murcia, Spain
    and
    Faculty of Applied Mathematics
    AGH University of Science and Technology
    Al. Mickiewicza 30
    30-059 Kraków, Poland
    e-mail

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