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arXiv · 2506.01518

Typical Uniqueness in Ergodic Optimization

Oliver Jenkinson·Xiaoran Li·Yuexin Liao·Yiwei Zhang
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Abstract

For ergodic optimization on any topological dynamical system, with real-valued potential function $f$ belonging to any separable Banach space $B$ of continuous functions, we show that the $f$-maximizing measure is typically unique, in the strong sense that a countable collection of hypersurfaces contains the exceptional set of those $f\in B$ with non-unique maximizing measure. This strengthens previous results asserting that the uniqueness set is both residual and prevalent.

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Oliver Jenkinson, Xiaoran Li, Yuexin Liao, Yiwei Zhang. 2025-06-02. Typical Uniqueness in Ergodic Optimization. https://arxiv.org/abs/2506.01518

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