2:17 PM
@MartinSleziak I went ahead and edited the tags on that question, mainly to get rid of . I am pretty sure that the choice of the tags could be improved, but I am not really sure which tags to add.

8 hours later…
10:38 PM
A new tag was created by caffeinemachine.
1

Definitions A topological dynamical system is a pair $(X, T)$ where $X$ is a compact metric space and let $T:X\to X$ is a continuous map. By the forward-orbit of a point $x$ in $X$ we mean the set $O_x=\{T^nx:\ n=1, 2, 3, ...\}$. We say that a point $x$ in $X$ is generic if $\bar O_x$ (closure...

In mathematics, topological dynamics is a branch of the theory of dynamical systems in which qualitative, asymptotic properties of dynamical systems are studied from the viewpoint of general topology. == Scope == The central object of study in topological dynamics is a topological dynamical system, i.e. a topological space, together with a continuous transformation, a continuous flow, or more generally, a semigroup of continuous transformations of that space. The origins of topological dynamics lie in the study of asymptotic properties of trajectories of systems of autonomous ordinary differential...