A completion construction for continuous dynamical systems

José Manuel García Calcines, Luis Javier Hernández Paricio, María Teresa Rivas Rodríguez

Abstract


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 dynamical
system. 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 are
homeomorphisms we have the class of $\check{C}_{0}^{\mathbf{r}}$-complete and
$\check{C}_{0}^{\mathbf{l}}$-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.).


Keywords


Dynamical system; exterior space; exterior flow; limit flow; end flow; completion flow

Full Text:

FULL TEXT

Refbacks

  • There are currently no refbacks.

Partnerzy platformy czasopism