Speaker: 刘磊（山东大学）

Time: 10:00-11:00, Dec. 2  2024

Online: Zoom: 811 5638 1768（Password: msrc）

Venue: 至善楼602

Title: Non-resonant Hopf links near a Hamiltonian equilibrium  (Joint with C. Grotta-Ragazzo and P. A. S. Salomao)

Abstract:

The aim of this talk is to present explicit conditions on the Birkhoff-Gustvason normal form of a two-degree-of-freedom Hamiltonian system near an equilibrium point, then ensure the existence of infinitely many periodic orbits on every sphere-like component of the energy surface near the equilibrium point. The equilibrium is supposed to be a nondegenerate minimum of the Hamiltonian. Every sphere-like component of the energy surface that sufficiently close to the equilibrium will contains at least two periodic orbits forming a Hopf link. The method is to check a certain non-resonance condition in HMS2015 on the rotation numbers for the Hopf link, and then infinitely many periodic orbits follow. This method is not making use of any global surface of section, as in HWZ1998. This results is then applied to the spatial isosceles three-body problem and Hill's lunar problem.