Entropies of random transformations on a non-compact space (Q2311968)

This paper concerns random dynamical systems on Polish spaces that are not necessarily compact. In this setting several notions of entropy are extended: Bowen's topological entropy, metric entropy, Brin-Katok local entropy, Katok \(\delta\)-entropy, and the topological entropy by \textit{R. L. Adler} et al. [Trans. Am. Math. Soc. 114, 309--319 (1965; Zbl 0127.13102)]. Moreover, classical results by \textit{M. Brin} and \textit{A. Katok} [Lect. Notes Math. 1007, 30--38 (1983; Zbl 0533.58020)] for the local entropy and by \textit{A. Katok} [J. Mod. Dyn. 1, No. 4, 545--596 (2007; Zbl 1149.37001)] for the \(\delta\)-entropy are reformulated in this context. A variational principle is considered as well.