Entropy of semigroup actions on commutative normed semigroups
报告人:Professor Dikran Dikranjan,Universit`a di Udine 时间:2019年10月21日16:00
报告摘要:We define and discuss properties of an entropy for actions of an amenable cancellative semigroup G on a commutative normed semigroup S. We use then this entropy in order to obtain a unified approach to various entropies for for actions of G, like the topological one (when G acts on a compact topological space), the measure entropy (when G acts on a measure space), the algebraic one (when G acts on an abelian group), the set theoretic one (when G acts on a set), etc In case of a finitely generated (not necessarily amenable) semigroup G, we discuss also an alternative definition of entropy (receptive entropy), adapted by Ghys, Langevin and Walczak in 1988 and later by Hofmann and Stoyanov in 1994, as well as Bis and Urbanski in 2004. This entropy remains positive in many case when the usual one vanishes.