Description

• Title:
  A completion construction for continuous dynamical systems
• Creator:
  Calcines, José Manuel García;
  Paricio, Luis Javier Hernández;
  Rodríguez, María Teresa Rivas
• Description:
  In this work we use the theory of exterior spaces to construct a~$\check{C}_{0}^\mathbf{r}$-completion and a $\check{C}_{0}^\mathbf{l}$-completion of a dynamicalsystem. If $X$ is a~flow, we construct canonical maps $X\to\check{C}_{0}^\mathbf{lr(X)$ and $X\to \check{C}_{0}^{\mathbf{l}}(X)$ and when these maps arehomeomorphisms we have the class of $\check{C}_{0}^{\mathbf{r}}$-complete and$\check{C}_{0}^{\mathbf{l}}$-complete flows, respectively. In this study we findout many relations between the topological properties of thecompletions and the dynamical properties of a given flow. In thecase of a complete flow this gives interesting relations betweenthe topological properties (separability properties, compactness,convergence of nets, etc.) and dynamical properties (periodicpoints, omega limits, attractors, repulsors, etc.).
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2016.04.12
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 44, No 2 (December 2014); 497 - 526;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2014.058/8175
• Subject:
  Dynamical system;
  exterior space;
  exterior flow;
  limit flow;
  end flow;
  completion flow;
  54H20;
  37B99;
  18B99;
  18A40
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2014.058
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other