Typical Uniqueness in Ergodic Optimization
Dynamical Systems
2025-06-03 v1
Abstract
For ergodic optimization on any topological dynamical system, with real-valued potential function belonging to any separable Banach space of continuous functions, we show that the -maximizing measure is typically unique, in the strong sense that a countable collection of hypersurfaces contains the exceptional set of those with non-unique maximizing measure. This strengthens previous results asserting that the uniqueness set is both residual and prevalent.
Cite
@article{arxiv.2506.01518,
title = {Typical Uniqueness in Ergodic Optimization},
author = {Oliver Jenkinson and Xiaoran Li and Yuexin Liao and Yiwei Zhang},
journal= {arXiv preprint arXiv:2506.01518},
year = {2025}
}