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 $X\to \check{C}_{0}^{\mathbf{r}}(X)$ 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.).
Citation
José M. García Calcines. Luis J. Hernández Paricio. María T. Rivas Rodríguez. "A completion construction for continuous dynamical systems." Topol. Methods Nonlinear Anal. 44 (2) 497 - 526, 2014.