The Conley-Zehnder indices of the rotating Kepler problem

Details The Conley-Zehnder indices of the rotating Kepler problem The Conley-Zehnder indices of the rotating Kepler problem

2012-01-10

arxiv.org/abs/1201.2032v1

Mathematics

Symplectic Geometry

18 pages, 3 figures

Scientific paper

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.

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