Representation of dynamical systems by Lipschitz functions

：Jonatan Gutman（波兰科学院数学所）
：2025-02-25 10:00
：海韵园实验楼S102

报告人：Jonatan Gutman（波兰科学院数学所）

时  间：2025年2月25日10:00

地  点：海韵园实验楼S102

内容摘要:

It is natural to consider the space of continuous functions on the real line C(R,R) as a dynamical system w.r.t.translation in time. Not surprisingly this point of view is ubiquitous in mathematics, notable examples are given by various spaces of almost periodic functions studied by Besicovitch, Bochner, Weyl, von Neumann and others. A celebrated result of Bebutov and Kakutani states that C(R,R) is a universal embedding space for all topological flows whose fixed point set embeds in the unit interval. In 1973 Eberlein showed that the compact space of 1-Lipschitz functions from the real line to the unit interval, is a topological model for all free measurable flows. This served as a fundamental step in his proof - together with Denker - of the Jewett-Krieger theorem for flows (1974), demonstrating the usefulness of the Lipschitz representation approach. We generalize Eberlein’s theorem to multidimensional flows, in particular giving a new proof for the one-dimensional case. This necessitates the development of several new tools such as a multidimensional version of a Lipschitz representation theorem by Gutman, Jin and Tsukamoto (2019) and a strengthening of Katok’s special representation theorem (1977). The theory of topological local sections also plays a role in the proof. Based on a joint work with Qiang Huo.

个人简介：

Jonatan Gutman，波兰科学院数学所副教授。博士毕业于耶路撒冷希伯来大学（导师B. Weiss）。研究方向为动力系统，已在Inventiones Math., GAFA, IMRN, CMP, Trans., Adv., JFA等杂志发表多篇文章。

 

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