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Typicality of periodic optimization over an expanding circle map

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arxiv 2501.10949 v3 pith:RKDMYZKC submitted 2025-01-19 math.DS

Rui Gao , Weixiao Shen , Ruiqin Zhang This is my paper
classification math.DS
keywords circleexpandingmaximizingmeasureoptimizationperiodicuniqueanalytic
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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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  1. Typical Uniqueness in Ergodic Optimization

    math.DS 2025-06 conditional novelty 6.0 of 10

    In ergodic optimization, for any separable Banach space of potentials densely embedded in C(X), the non-unique-maximizing functions lie in a countable union of hypersurfaces.

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