Relativization of dynamical properties
The author presents recent developments in the relative topological dynamics. Mainly, he reviews some recent results on the relative Li-York chaos, relative topological entropy, relative variational principle, relative entropy pair, relative topological Pinsker factor, relative positive entropy and relative uniform positive entropy. Let us recall that for any topological dynamical system \((X,T)\), where \(X\) is a metric compact space and \(T\) a homeomorphism on \(X\), the dynamical system \((Y,S)\) is said to be a factor of \(X\) if there is a continuous surjective map \(\pi\) from \(X\) to \(Y\) such that \(\pi \circ T= S \circ \pi\). The dynamical property holds relatively if it holds relatively with respect to the factor map \(\pi\).
scientific article; zbMATH DE number 6131969
scientific article