Variational principles for topological entropies of subsets

De-Jun Feng, Wen Huang

Let $(X,T)$ be a topological dynamical system. We define the measure-theoretical lower and upper entropies ${\underline{h}}_{\mu }(T)$, ${\bar{h}}_{\mu }(T)$ for any $\mu \in M(X)$, where $M(X)$ de…