Transition Tori in the Planar Restricted Elliptic Three Body Problem

@inproceedings{Capinski2009TransitionTI,
  title={Transition Tori in the Planar Restricted Elliptic Three Body Problem},
  author={Maciej J. Capinski and Piotr Zgliczynski},
  year={2009}
}
We consider the elliptic three body problem as a perturbation of the circular problem. We show that for sufficiently small eccentricities of the elliptic problem, and for energies sufficiently close to the energy of the libration point L2, a Cantor set of Lyapounov orbits survives the perturbation. The orbits are perturbed to quasi-periodic invariant tori. We show that for a certain family of masses of the primaries, for such tori we have transversal intersections of stable and unstable… CONTINUE READING

Citations

Publications citing this paper.
SHOWING 1-10 OF 12 CITATIONS

References

Publications referenced by this paper.
SHOWING 1-10 OF 29 REFERENCES

Proof of A.N. Kolmogorov’s theorem on the preservation of quasi-periodic motions under small perturbations of the Hamiltonian

  • V. I. Arnold
  • Usp. Mat. Nauk
  • 1963
Highly Influential
25 Excerpts

C

  • J. Llibre, R. Martinez
  • Simo,Transversality of the Invariant Manifolds…
  • 1985
Highly Influential
10 Excerpts

On the Generalization of a theorem of A

  • J. Moser
  • Liapounoff, Communications on Pure and Applied…
  • 1958
Highly Influential
14 Excerpts

R

  • M. Gidea
  • de la Llave, Topological methods in the…
  • 2006
Highly Influential
4 Excerpts

Orbits of unbounded energy in quasi-periodic perturbations of geodesic flows

  • A. Delshams, R.de la Llave, T. Seara
  • Adv. Math
  • 2006
1 Excerpt

R

  • X. Cabré, E. Fontich
  • de la Llave, The parameterization method for…
  • 2005

Similar Papers

Loading similar papers…