Skip to content
DraconiticResearch
Search Sources API
178,970 studies31 sourcesUpdated 20 min ago
PreprintCC BY-SA 4.0arXiv

Dynamics of planar integrable Kepler billiards with a focused hyperbolic branch

  • Daniel Jaud
  • Lei Zhao
Open at sourcePDFDOICite

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}.

Related

  1. Morse Bridge between Planar Kepler and Hyperbolic Landau Dynamics
    Mikhail S. Plyushchay
    arXivPreprintarXiv licenceFull textMathematical physicsHigh-energy & particle physicsarXiv
  2. Uniformly hyperbolic strictly convex billiards
    Wentao Fan, Boris Hasselblatt
    arXivPreprintCC0Full textDynamical systemsMathematical physicsarXiv
  3. Morse bridge between planar Kepler and hyperbolic Landau dynamics
    Mikhail S. Plyushchay
    Journal of High Energy PhysicsPeer-reviewedCC BY 4.0Full textMathematical physicsCrossref
  4. Hyperbolic scattering in the planar n-body problem
    Junhao Lie, Guowei Yu
    arXivPreprintarXiv licenceFull textDynamical systemsarXiv
  5. Menger Curve and Non-Planar Boundaries in Quotients of Hyperbolic Groups
    Rafaela Ioannou
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{jaud2026dynamics,
  title = {{Dynamics of planar integrable Kepler billiards with a focused hyperbolic branch}},
  author = {Daniel Jaud and Lei Zhao},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.18705},
  eprint = {2609.18705},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.18705},
  note = {CC BY-SA 4.0},
}
RIS
TY  - UNPB
TI  - Dynamics of planar integrable Kepler billiards with a focused hyperbolic branch
AU  - Daniel Jaud
AU  - Lei Zhao
PY  - 2026
DA  - 2026/09/16
PB  - arXiv
DO  - 10.48550/arxiv.2609.18705
UR  - https://arxiv.org/abs/2609.18705
AB  - 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}.
ER  -