应304am永利集团官网杨璐教授邀请,俄罗斯国立高等经济大学Alexey Kazakov教授将于2024年9月1日至9月6日访问我校并作系列学术报告。

报告题目一：On pseudohyperbolic attractors：notion and theory

时间：2024年9月6日（星期三）下午16: 00-17: 00

地点：大学生活动中心506报告厅

报告题目二：On pseudohyperbolic attractors：application and numerical methods

时间：2024年9月6日（星期三）下午17: 00-18: 00

地点：大学生活动中心506报告厅

报告摘要：One of the most fundamental problems in multidimensional chaos theory is the study of strange attractors which are robustly chaotic (i.e., they remain chaotic after small perturbations of the system). It was hypothesized that the robustness of chaoticity is equivalent to the pseudohyperbolicity of the attractor. Pseudohyperbolicity is a generalization of hyperbolicity. The main characteristic property of a pseudohyperbolic attractor is that each of its orbits has a positive maximal Lyapunov exponent. In addition, this property must be preserved under small perturbations. The foundations of the theory of pseudohyperbolic attractors were laid by Turaev and Shilnikov, who showed that the class of pseudohyperbolic attractors, besides the classical Lorenz and hyperbolic attractors, also includes wild attractors which contain orbits with a homoclinic tangency.

In this lectures, using the pseudohyperbolicity notion, we will explain how to check whether the attractor is robustly chaotic or not. We will describe the corresponding numerical methods and apply them for the study of model systems (the Lorenz, Lyubimov-Zaks, and Shimizu-Morioka systems) as well as systems arising in applications (optical laser model, model of thermal convection, ensembles of oscillators, etc.).

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报告人简介

Alexey Kazakov教授致力于非线性动力学和混沌理论的研究，曾在2016年获得Dmitry Zimin“Dynasty”基金会青年数学家竞赛奖项，2018-2019年获得俄罗斯基础研究基金会，2019-2020年获得俄罗斯基础研究基金会，2019-2024年获得俄罗斯基础研究基金会，2021年获得俄罗斯尼日尼诺夫哥罗德州科学与高等教育部颁发的荣誉证书，其卓越工作和贡献赢得了国际学术界的广泛认可。

Alexey Kazakov教授在非线性动力学领域发表了大量高水平的科研论文，涵盖了多个领域，其研究成果在Chaos、Nonlinearity、Commun. Nonlinear Sci. Numer. Simul.、Regul. Chaotic Dyn.等重要学术期刊上发表，并被广泛引用。

甘肃应用数学中心

甘肃省高校应用数学与复杂系统省级重点实验室

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萃英学院

2024年8月27日