Upper semi-continuity of entropy in non-compact settings

Funding: G.I. was partially supported by CONICYT PIA ACT172001 and by Proyecto Fondecyt 1190194.We prove that the entropy map for countable Markov shifts of finite entropy is upper semi-continuous on the set of ergodic measures. Note that the phase space is non-compact. We also discuss the related problem of existence of measures of maximal entropy.PostprintPeer reviewe