Year: 2016
Type: preprint
Abstract: In this note, we prove that below the first critical energy level, a proper combination of the Ligon-Schaaf and Levi-Civita regularization mappings provides a convex symplectic embedding of the energy surfaces of the planar rotating Kepler problem into $R^4$ endowed with its standard symplectic structure. A direct consequence is the dynamical convexity of the planar rotating Kepler problem, which has been established by Albers-Fish-Frauenfelder-van Koert by direct computations. This result opens up new approaches to attack the Birkhoff conjecture about the existence of a global surface of section in the restricted planar circular three body problem using holomorphic curve techniques.
Source: arXiv (Cornell University)
Authors: Frauenfelder, Urs, van Koert, Otto, Zhao, Lei
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2399879620