数学科学学院学术报告

--- 基础数学系学术报告 及 分析、偏微分方程与动力系统讨论班 (2025春季第3讲)

Non-uniformly hyperbolic endomorphisms equations

Martin Andersson 

(巴西弗鲁米嫩塞联邦大学)

时间：5月13日（周二）上午9:30-10:30

地点：沙河校区国实E803

摘要: Consider a non-invertible linear endomorphism of the two torus (e.g. an expanding map). Is it possible to deform it through homotopy to obtain a map which preserves the Haar measure and has a negative Lyapunov exponent almost everywhere? If so, can the Lyapunov exponents be as far away from zero as we want? We give a positive answer to both questions, provided that the topological degree is not too small. As a consequence, we are able to conclude that the Standard Map composed with an expanding map of sufficiently large degree is non-uniformly hyperbolic for large parameters. This is a joint work with Pablo Carraso and Radu Saghin.

报告人简介: Martin Andersson教授博士毕业于纯粹与应用数学研究所（IMPA），曾在北京国际数学中心进行博士后工作，现任教于弗鲁米嫩塞联邦大学（Universidade Federal Fluminense）。Andersson教授长期从事微分动力系统与遍历论领域的研究，在部分双曲系统的持续遍历性、无理流的物理测度等课题上取得重要成果，相关学术成果发表于Advances in Mathematics、Transactions of AMS、Comm. Math. Phys.顶尖综合性数学期刊。

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