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arXiv · 2501.10949

Typicality of periodic optimization over an expanding circle map

Rui Gao·Weixiao Shen·Ruiqin Zhang
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Abstract

We study the ergodic optimization problem over a real analytic expanding circle map. We show that in both the topological and the measure-theoretical senses, a typical $C^r$ performance function has a unique maximizing measure and the unique maximizing measure is supported on a periodic orbit, for $r=1,2,\dots,\infty,\omega$.

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Rui Gao, Weixiao Shen, Ruiqin Zhang. 2025-01-19. Typicality of periodic optimization over an expanding circle map. https://arxiv.org/abs/2501.10949

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