谱几何与反问题讨论班——Lyapunov spectral rigidity of expanding circle maps

来源:数学科学学院 发布时间:2023-11-27   185

报告题目: Lyapunov spectral rigidity of expanding circle maps

报告人:Vadim Kaloshin(欧洲科学院院士)


地点: 海纳苑2210报告厅

报告人简介:Vadim Kaloshin,美国马里兰大学-帕克分校数学系Brin首席教授、奥地利科技学院讲席教授,欧洲科学院院士,曾获得美国科学院院士提名、西蒙斯奖等荣誉,现担任Adv. Math., Ergodic Theory Dynam. Systems等杂志编委,主要从事动力系统领域的研究,在国际上最顶尖的四大综合性数学期刊Acta Math., Ann. of Math., J. Amer. Math. Soc., Invent. Math.上公开发表高质量学术论文8篇,在Duke Math. J., Geom. Funct. Anal., J. Eur. Math. Soc (JEMS), Comm. Pure Appl. Math., Arch. Ration. Mech. Anal.等国际权威期刊上公开发表高水平学术论文65篇。

Abstract: Motivated by the question "Can you hear the shape of a drum?" and spectral rigidity for metrics for an expanding circle map of degree at least 2, we define Lyapunov spectrum as the set of all Lyapunov exponents (multipliers) at periodic orbits. This set is analogous to the unmarked length spectrum of negatively curved metrics on surfaces of genus at least 2. Is the following local rigidity holds: every C^r smooth expanding circle map f has a neighborhood (in C^r topology) such that any perturbation of f within this neighborhood that keeps the Lyapunov spectrum must be smoothly conjugate to f (subject to some sparsity assumption on the spectrum on f)? The answer is positive. The proof uses a novel iterative scheme which we will outline in the talk. This is joint work in progress with Kostya Drach.



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