Transverse foliations in the rotating Kepler problem

2023/11/02 by Kim, Seongchan
#Dynamical Systems (math.DS) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2311.01231

Abstract

We construct finite energy foliations and transverse foliations of neighbourhoods of the circular orbits in the rotating Kepler problem for all negative energies. This paper would be a first step towards our ultimate goal that is to recover and refine McGehee's results on homoclinics and to establish a theoretical foundation to the numerical demonstration of the existence of a homoclinic-heteroclinic chain in the planar circular restricted three-body problem, using pseudoholomorphic curves.

Related

• Transverse foliations for two-degree-of-freedom mechanical systems
• Finite energy foliations in the restricted three-body problem
• A convex embedding for the rotating Kepler problem
• The special concave toric domain for the rotating Kepler problem
• Pseudo-holomorphic dynamics in the restricted three-body problem