Felipe García-Ramos, Hanfeng Li
This paper is a survey about recent developments in the local entropy theory for topological dynamical systems and continuous group actions, with particular emphasis on the connections with other areas of dynamical systems and mathematics.
This paper contains 19 sections, 56 theorems, 47 equations.
Proposition 2.1
If $\pi\colon {G \curvearrowright X} \to G\curvearrowright Y$ is a factor map then is a closed $G$-invariant equivalence relation. Conversely, if $Q\subset X\times X$ is a closed $G$-invariant equivalence relation then $\pi\colon {G \curvearrowright X} \to G\curvearrowright X/Q$ is a factor map where $G\curvearrowright X/Q$ is the induced action $gy=\pi(g\pi^{-1}(y))$.
