The Conley-Zehnder indices of the rotating Kepler problem

• Main Authors: Albers, Peter, Fish, Joel W, Frauenfelder, Urs, van Koert, Otto
• Format: Journal Article
• Language: English
• Published: 10-01-2012
• Subjects: Mathematics - Dynamical Systems; Mathematics - Symplectic Geometry
• DOI: 10.48550/arxiv.1201.2032

Mathematical Proceedings of the Cambridge Philosophical Society,
(2013), 243 - 260 We determine the Conley-Zehnder indices of all periodic orbits of the
rotating Kepler problem for energies below the critical Jacobi energy.
Consequently, we show the universal cover of the bounded component of the
regularized energy hypersurface is dynamically convex. Moreover, in the
universal cover there is always precisely one periodic orbit with
Conley-Zehnder index 3, namely the lift of the doubly covered retrograde
circular orbit.