We prove that the entropy map for countable Markov shifts of finite entropy is upper semi-continuous at ergodic measures. Note that the phase space is non-compact. Applications to systems that can be coded by these shifts, such as positive entropy diffeomorphisms on compact manifolds, are given. We also discuss the related problem of existence of measures of maximal entropy.
No takes yet. Share an insight, caveat, or question.
Iommi et al. (2020) studied this question.
Synapse has enriched 5 related papers. Consider them for comparative context: