Introduction to Dynamical Renormalization
The ideas of renormalization were introduced into the theory of dynamical systems by M. Feigenbaum almost 50 years ago. By now renormalization is one of the main methods of studying asymptotic behavior of dynamical systems.
In this course we will introduce the ideas of the renormalization theory in different settings, including unimodal maps, homeomorphisms of the unit circle, KAM theory to name a few. We shall also discuss Ergodic theory aspects of renormalization, the thermodynamic formalism, and basic results in the theory of hyperbolic dynamical systems. It is expected that by the end of the course students will be able to take on research projects focused on renormalization and related problems.
In this course we will introduce the ideas of the renormalization theory in different settings, including unimodal maps, homeomorphisms of the unit circle, KAM theory to name a few. We shall also discuss Ergodic theory aspects of renormalization, the thermodynamic formalism, and basic results in the theory of hyperbolic dynamical systems. It is expected that by the end of the course students will be able to take on research projects focused on renormalization and related problems.
讲师
日期
2024年09月18日 至 12月11日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周二,周三 | 15:20 - 16:55 | Shuangqing-B725 | ZOOM 04 | 482 240 1589 | BIMSA |
修课要求
None
视频公开
公开
笔记公开
公开
讲师介绍
康斯坦丁·卡宁（Konstantin Khanin）在莫斯科朗道理论物理研究所获得博士学位，并于1994年之前一直担任该所的研究员。此后，他先后在普林斯顿大学、剑桥大学艾萨克·牛顿数学科学研究所和赫瑞-瓦特大学任教，之后加入多伦多大学担任教职。
卡宁曾于2000年受邀在巴塞罗那举行的欧洲数学大会（European Congress of Mathematics）上作报告；2013年成为西蒙斯基金会（Simons Foundation）会士；2017年担任法国国际数学研究中心（CIRM）的让-莫莱（Jean-Morlet）讲席教授；2018年受邀在里约热内卢举办的国际数学家大会（ICM）上作报告。2021年，他荣获洪堡奖（Humboldt Prize，又称洪堡研究奖），以表彰其毕生在数学研究领域取得的杰出成就。