Ergodic Maximizing Measures of Non-Generic, Yet Dense Continuous Functions
Dynamical Systems
2017-04-20 v1
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.
Cite
@article{arxiv.1704.05616,
title = {Ergodic Maximizing Measures of Non-Generic, Yet Dense Continuous Functions},
author = {Mao Shinoda},
journal= {arXiv preprint arXiv:1704.05616},
year = {2017}
}