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arXiv · 2609.18705

Dynamics of planar integrable Kepler billiards with a focused hyperbolic branch

Daniel Jaud·Lei Zhao
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Abstract

We consider the integrable dynamics of a planar Kepler billiard in the plane bounded by a branch of a hyperbola focused at the Kepler center. As a sequel to our previous work \cite{JZ2}, we use the existence of the foci-caustic circle to identify an elliptic curve on which the dynamics is linearized and we analyze Cayley's condition on $n$-periodic orbits in this setting. By taking various limits also we discuss the dynamics of planar Kepler billiards with boundary being a focused parabolic arc, as well as a straight line. In this last case, our approach offers a different way to deduce the elliptic curve as in \cite{Felder}.

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Daniel Jaud, Lei Zhao. 2026-09-16. Dynamics of planar integrable Kepler billiards with a focused hyperbolic branch. https://arxiv.org/abs/2609.18705

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