报告人: Victor Ginzburg教授

 University of California Santa Cruz, US

题目: Periodic orbits of Hamiltonian systems: the Conley conjecture and pseudo-rotations

时间:2018年05月18日 14:30

地点：海韵实验楼105

摘要：One distinguishing feature of Hamiltonian dynamical systems -- a class of systems naturally arising in many physics problems -- is that such systems, with very few exceptions, tend to have numerous periodic orbits. In 1984 Conley conjectured that a Hamiltonian diffeomorphism (i.e., the time-one  map of a Hamiltonian flow) of a torus has infinitely many periodic orbits. This  conjecture was proved by Hingston some twenty years later and similar results for surfaces other than the sphere were established by Franks and Handel. Of course, one can expect the Conley conjecture to hold for a much broader class of phase spaces, and this is indeed the case as has been shown by Gurel, Hein and the speaker. However, the conjecture is known to fail for some, even very simple, phase spaces such as the sphere. These spaces admit Hamiltonian diffeomorphisms with finitely many periodic orbits -- the so-called pseudo-rotations -- which are of particular interest in dynamics.

In this talk, based on the results of Gurel and the speaker, we will examine underlying reasons for the existence of periodic orbits for Hamiltonian systems and discuss the situations where the Conley conjecture does not hold.

报告人简介：Victor (Viktor) Ginzburg, 美国加州大学圣克鲁兹分校教授、数学系系主任。1990年在加州大学伯克立分校获得数学博士。先后曾在伯克立数学研究所、斯坦福大学、普林施顿高等研究所等做博士后及访问。他近期主要研究辛拓扑和Hamitonian dynamics方面的Hamiltonian Seifert Conjecture, the Conley Conjecture等问题. 曾在Annals of Mathematics, Journal of the American Mathematical Society, Duke Mathematical Journal等发表多篇论文。

联系人:谭绍滨教授、余铌娜助理教授

欢迎广大师生参加！