R304, Astronomy-Mathematics Building, NTU
Speaker(s):
Chih-Hung Chang (National University of Kaohsiung)
Lien-Yung Kao (George Washington University)
Bing Li (South China University of Technology)
Organizer(s):
Jung-Chao Ban (National Chengchi University)
一、 課程背景與目的：
動態系統是目前發展非常活躍的學科之一。近一個世紀的發展，動態系統已有長足的進步並將觸角深入各個領域，除了物理及資訊科學外，在傳統數學領域也有相當大程度的發展及應用。本課程主要有兩個目的，第一是藉由該系列課程來引進目前動態系統一些熱門且新穎研究給國內學生及有興趣的學者知悉，特別著重在和幾個傳統數學領域的深刻聯繫，其中包括了數論、幾何以及代數；第二個目的是希望於今年五月NCTS動態系統會議前提供完整的先備知識給與會者，非常歡迎有興趣的師生參加。
二、 課程之大綱：
The aim of these four-hour mini-courses is to provide a rough view of arithmetic dynamics, topological dynamics and ergodic geometry. For the arithmetic dynamics, Professor Li will provide the basic knowledge of the Fourier dimension and its connection to the Salem set; Professor Liao will talk about the dynamics of the polynomial and rational maps of p-adic numbers and show that the polynomials with p-adic integer coefficients and rational maps with good reduction are 1-Lipschitz and their dynamical structures are described by a decomposition of the space into finitely many periodic orbits, countably many minimal subsystems and the attracting basins of the aforementioned two parts. For the topological dynamics, Professor Chang will introduce the concept of SFT on groups and investigate its periodicity. For the ergodic geometry, Professor Kao focus on the geometry and dynamics of hyperbolic surfaces and show how thermodynamics is used to characterize dynamics and some geometric quantities of the hyperbolic geometry.
三、 講題：
5/10
Speaker：Bing Li (South China University of Technology, China)
Title：Fourier Dimension and Salem Sets
5/13
Speaker: Lien-Yung Kao (The University of Chicago, US)
Title：Geometry and Dynamics of Hyperbolic Surfaces
5/17 (only 10:00-12:00)
Speaker：Chih-Hung Chang (National University of Kaohsiung, Taiwan)
Title：Periodicity of Shifts over Groups (I)
5/20
Speaker：Chih-Hung Chang (National University of Kaohsiung, Taiwan)
Title：Periodicity of Shifts over Groups (II)
