Intrinsic ergodicity via obstruction entropies

Abstract

Bowen showed that a continuous expansive map with specification has a unique measure of maximal entropy. We show that the conclusion remains true under weaker non-uniform versions of these hypotheses. To this end, we introduce the notions of obstructions to expansivity and specification, and show that if the entropy of such obstructions is smaller than the topological entropy of the map, then there is a unique measure of maximal entropy.

17 pages, small changes to previous numbering due to minor changes in exposition

References in corpus (2)

• Intrinsic ergodicity beyond specification: beta-shifts, S-gap shifts, and their factors
• Topological pressure of simultaneous level sets

Cited by in corpus (5)

• Unique equilibrium states for flows and homeomorphisms with non-uniform structure
• Large deviations for systems with non-uniform structure
• On subshifts with slow forbidden word growth
• Continuum-wise hyperbolicity, periodic shadowing, and measures of maximal entropy
• Ergodic optimization for continuous functions on non-Markov shifts