New and old facts about entropy in uniform spaces and topological groups (Q409709)

This paper gives an overview of the relationships between several different natural notions of entropy for maps: the topological entropy of continuous maps on compact spaces, \textit{R. Bowen}'s extension to uniformly continuous maps on metric spaces [Trans. Am. Math. Soc. 153, 401--414 (1971; Zbl 0212.29201)] and its subsequent extension to uniformly continuous maps on uniform spaces, and finally the algebraic entropy for continuous automorphisms of locally compact groups introduced by \textit{J. Peters} [Adv. Math. 33, 1--13 (1979; Zbl 0421.28019)] and its subsequent extensions and generalisations. The literature is surveyed, and some of the relationships lacking accurate proofs in the literature are clarified.