Ergodic Maximizing Measures of Non-Generic, Yet Dense Continuous Functions

Abstract

Ergodic optimization aims to single out dynamically invariant Borel probability measures which maximize the integral of a given "performance" function. For a continuous self-map of a compact metric space and a dense set of continuous performance functions, we show that the existence of uncountably many ergodic maximizing measures. We also show that, for a topologically mixing subshift of finite type and a dense set of continuous functions there exist uncountably many ergodic maximizing measures which are fully supported and have positive entropy.

References in corpus (2)

• Ergodic optimization, zero temperature limits and the max-plus algebra
• Path connectedness and entropy density of the space of ergodic hyperbolic measures