报告题目: Prevalence in Ergodic optimization, and its relationship to the (non)-Sturiman maximizing problems for doubling maps

报告人:张一威，华中科技大学

时间：9月5日（星期三）下午4：00--5：00

地点：东区管理科研楼  数学科学学院1418室

摘要: Given a dynamical system, we say that a performance function has property P if its time averages along orbits are maximized at a periodic orbit. It is conjectured by several authors that for sufficiently hyperbolic dynamical systems, property P should be typical among sufficiently regular performance functions. In this paper we address this problem using a probabilistic notion of typicality that is suitable to infinite dimension: the concept of prevalence as introduced by Hunt, Sauer, and Yorke. For the one-sided shift on two symbols, we prove that property P is prevalent in spaces of functions with a strong modulus of regularity. Our proof uses Haar wavelets to approximate the ergodic optimization problem by a finite-dimensional one, which can be conveniently restated as a maximum cycle mean problem on a de Bruijin graph.

If time permits, we will also disucuss the applications of the above comintorical optimization methods in dealing with (non)-Sturiman maximizing (open) problems for doubling maps.

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