Shadowing in actions of some Abelian groups

Volume 179 / 2003

Sergei Yu. Pilyugin, Sergei B. Tikhomirov Fundamenta Mathematicae 179 (2003), 83-96 MSC: 37C50, 22F05. DOI: 10.4064/fm179-1-7

Abstract

We study shadowing properties of continuous actions of the groups ${\mathbb Z}^p$ and ${\mathbb Z}^p\times {\mathbb R}^p$. Necessary and sufficient conditions are given under which a linear action of ${\mathbb Z}^p$ on ${\mathbb C}^m$ has a Lipschitz shadowing property.

Authors

  • Sergei Yu. PilyuginFaculty of Mathematics and Mechanics
    St. Petersburg State University
    Bibliotechnaya pl., 2
    198904, St. Petersburg, Russia
    e-mail
  • Sergei B. TikhomirovFaculty of Mathematics and Mechanics
    St. Petersburg State University
    Bibliotechnaya pl., 2
    198904, St. Petersburg, Russia

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