中科院数学与系统科学研究院

数学研究所

动力系统研讨班报告

报告人：Prof. Kuo-Chang Chen(National Tsinghua University, Taiwan)

题  目：Heteroclinic orbits of the n-center problem

时  间：2019.09.03（星期二）, 16:00-17:00

地  点：数学院南楼N226室

摘  要：It is well-known that the N-center problem is chaotic when N ≥ 3. By regularizing collisions, one can associate the dynamics with a symbolic dynamical system which yields infinitely many periodic and chaotic orbits, possibly with collisions. it is a challenging task to construct chaotic orbits without any collision. In this talk we consider the planar N-center problem with collinear centers and N ≥ 4, and show that, for any fixed nonnegative energy and certain types of periodic free-time minimizers, there are infinitely many collision-free heteroclinic orbits connecting them. Our approach is based on minimization of a normalized action functional over paths within certain topological classes, and the exclusion of collision is based on some recent advances on local deformation methods. This is a joint work with Guowei Yu.