A completion construction for continuous dynamical systems

  1. García Calcines, J.M. 1
  2. Hernández Paricio, L.J. 2
  3. Rivas Rodríguez, M.T. 2
  1. 1 Universidad de La Laguna
    info

    Universidad de La Laguna

    San Cristobal de La Laguna, España

    ROR https://ror.org/01r9z8p25

  2. 2 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Zeitschrift:
Topological Methods in Nonlinear Analysis

ISSN: 1230-3429

Datum der Publikation: 2014

Ausgabe: 44

Nummer: 2

Seiten: 497-526

Art: Artikel

SCOPUS: 2-s2.0-84921832233 WoS: WOS:000348243000011 GOOGLE SCHOLAR

Andere Publikationen in: Topological Methods in Nonlinear Analysis

Zusammenfassung

In this work we use the theory of exterior spaces to construct a (Formula Presented)-completion and a (Formula Presented)-completion of a dynamical system. If X is a flow, we construct canonical maps (Formula Presented) and (Formula Presented) and when these maps are homeomorphisms we have the class of (Formula Presented)-complete and (Formula Presented) -complete flows, respectively. In this study we find out many relations between the topological properties of the completions and the dynamical properties of a given flow. In the case of a complete flow this gives interesting relations between the topological properties (separability properties, compactness, convergence of nets, etc.) and dynamical properties (periodic points, omega limits, attractors, repulsors, etc.).