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arXiv · 2502.12269

Joint typical periodic optimization

Zelai Hao·Yinying Huang·Oliver Jenkinson·Zhiqiang Li
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Abstract

We prove a generalised Yuan--Hunt--Ma\~n\'e Conjecture: if $\mathcal{F}$ is the Banach space of $\alpha$-H\"older functions, and $\mathcal{T}$ is either a space of Lipschitz expanding maps, or of Anosov diffeomorphisms, or the family of beta-transformations on the interval, there is an open dense subset of $\mathcal{T}\times\mathcal{F}$ consisting of map-function pairs whose maximizing invariant measure is unique and supported on a periodic orbit.

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Zelai Hao, Yinying Huang, Oliver Jenkinson, Zhiqiang Li. 2025-02-17. Joint typical periodic optimization. https://arxiv.org/abs/2502.12269

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