Description

• Title:
  Weak forms of shadowing in topological dynamics
• Creator:
  Cherkashin, Danila;
  Kryzhevich, Sergey
• Description:
  We consider continuous maps of compact metric spaces. It is proved that every pseudotrajectory with sufficiently small errors contains a subsequence of positive density that is point-wise close to a subsequence of an exact trajectory with the same indices. Also, we study homeomorphisms such that any pseudotrajectory can be shadowed by a finite number of exact orbits. In terms of numerical methods this property (we call it multishadowing) implies possibility to calculate minimal points of the dynamical system. We prove that for the non-wandering case multishadowing is equivalent to density of minimal points. Moreover, it is equivalent to existence of a family of $\varepsilon$-networks ($\varepsilon > 0$) whose iterations are also $\varepsilon$-networks. Relations between multishadowing and some ergodic and topological properties of dynamical systems are discussed.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2017 Topological Methods in Nonlinear Analysis
• Date:
  2017.07.07
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 50, No 1 (September 2017); 125 - 150;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2017.020/12386 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2017.020/12387
• Subject:
  Topological dynamics;
  minimal points;
  invariant measure;
  shadowing;
  chain recurrence;
  $\varepsilon$-networks;
  syndetic sets;
  Primary;
  37B05;
  Secondary;
  37B20;
  37A05
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2017.020
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other