The Conley-Zehnder indices of the rotating Kepler problem

Abstract

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.

18 pages, 3 figures

References in corpus (3)

• The contact geometry of the restricted 3-body problem
• Global surfaces of section in the planar restricted 3-body problem
• The Cartan geometry of the rotating Kepler problem

Cited by in corpus (12)

• Global surfaces of section in the planar restricted 3-body problem
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• Fiberwise Convexity of Hill's lunar problem
• On a convex embedding of the Euler problem of two fixed centers
• Real holomorphic curves and invariant global surfaces of section
• $J^{+}$-like invariants of periodic orbits of the second kind in the restricted three body problem
• On families of periodic orbits in the restricted three-body problem
• Global surfaces of section for Reeb flows in dimension three and beyond
• Some remarks on symmetric periodic orbits in the restricted three-body problem
• Spectrum estimates of Hill's lunar problem
• Bifurcations of symmetric periodic orbits via Floer homology
• The special concave toric domain for the rotating Kepler problem