Prevalent uniqueness in ergodic optimisation
Dynamical Systems
2020-03-20 v1
Abstract
One of the fundamental results of ergodic optimisation asserts that for any dynamical system on a compact metric space and for any Banach space of continuous real-valued functions on which embeds densely in there exists a residual set of functions in that Banach space for which the maximising measure is unique. We extend this result by showing that this residual set is additionally prevalent, answering a question of J. Bochi and Y. Zhang.
Cite
@article{arxiv.2003.08762,
title = {Prevalent uniqueness in ergodic optimisation},
author = {Ian D. Morris},
journal= {arXiv preprint arXiv:2003.08762},
year = {2020}
}