A completion construction for continuous dynamical systems
Keywords
Dynamical system, exterior space, exterior flow, limit flow, end flow, completion flowAbstract
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.).
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