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Variational construction for homoclinic and heteroclinic orbits in the N-center problem
余国巍(南开大学陈省身数学研究所,特聘研究员)
1月6日10:30-11:30  闵行数学楼102报告厅

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 ≥ 3, 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 Kuo-Chang Chen.

报告人简介: 余国巍,南开大学陈省身数学研究所,特聘研究员。毕业于美国明尼苏达大学获博士学位。曾先后任职于加拿大多伦多大学,法国巴黎九大/巴黎天文台,意大利都灵大学,美国数学科学研究所(MSRI),从事博士后研究。研究方向为动力系统,天体力学和变分法。

邀请人:张静