arXiv subjects

Yinying Huang

Publications and source records attributed to Yinying Huang.

3 recordsLinked to original sources

arXiv2026

Joint typical periodic optimization: systems with stable hyperbolicity

The framework of joint typical periodic optimization, in which both the dynamical system and the potential function are allowed to vary simultaneously, was introduced in [HHJL25], in a direction motivated by the work of Yang, Hunt & Ott [YHO00]. For certain classes of hyperbolic systems, it was shown there that optimizing periodic orbits persist under simultaneous perturbation, yielding joint locking sets that contain open dense subsets of the relevant product spaces. In the present article we broaden the scope of this theory, by developing an axiomatic joint perturbation framework that accommodates a wider class of stably hyperbolic systems, and by establishing new joint typical periodic optimization results for several natural and important families: Axiom A diffeomorphisms with the no-cycle property, hyperbolic rational maps on the Riemann sphere, real quadratic polynomials, and $C^r$ maps in one dimension.

math.DS↗

arXiv2026

Joint typical periodic optimization

We prove a generalised Yuan--Hunt--Mañé Conjecture: if $\mathcal{F}$ is the Banach space of $α$-Hölder 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.

math.DS↗

arXiv2025

Ergodic optimization for Gauss's continued fraction map

The theory of ergodic optimization for distance-expanding maps is extended to Gauss's continued fraction map. Since the set of invariant probability measures is not weak$^*$ closed, we establish a characterisation of the closure of this set, and investigate limit-maximizing measures for Hölder continuous functions. Although a Mañé cohomology lemma is shown to hold, the typical periodic optimization conjecture is shown to fail, as a consequence of the typical finite optimization property established for a certain class of (rationally maximized) functions. The typical periodic optimization (TPO) property is shown to hold, however, for the class of $α$-Hölder essentially compact functions.

math.DS↗