Stable manifolds associated to fixed points with linear part equal to identity

  title={Stable manifolds associated to fixed points with linear part equal to identity},
  author={Immaculada Baldom{\'a} and Ernest Fontich},
We consider maps defined on an open set of Rnþm having a fixed point whose linear part is the identity. We provide sufficient conditions for the existence of a stable manifold in terms of the nonlinear part of the map. These maps arise naturally in some problems of Celestial Mechanics. We apply the results to prove the existence of parabolic orbits of the spatial elliptic three-body problem. r 2003 Elsevier Inc. All rights reserved. 


Publications referenced by this paper.
Showing 1-10 of 17 references

Melnikov method and transversal homoclinic orbits in the restricted three-body problem

  • Z. Xia
  • J. Differential Equations 96 (1992) 170–184…
  • 2004
1 Excerpt

Stable curves asymptotic to a degenerate fixed point

  • E. Fontich
  • Nonlinear Anal. 35 (1999) 711–733. ARTICLE IN…
  • 2004
3 Excerpts

Heteroclinic orbits and Bernoulli shift for the elliptic collision restricted threebody problem

  • M. Álvarez, J. Llibre
  • Arch. Rational Mech. Anal. 156
  • 2001
2 Excerpts

The tetrahedral 4-body problem

  • J. Delgado, C. Vidal
  • J. Dynamics Differential Equations 11 (4)
  • 1999
2 Excerpts

Parabolic orbits in the elliptic restricted three body problem

  • R. Martı́nez, C. Pinyol
  • J. Differential Equations
  • 1994
3 Excerpts

Invariant manifolds for a class of parabolic points

  • J. Casasayas, E. Fontich, A. Nunes
  • Nonlinearity 5
  • 1992
1 Excerpt

Heteroclinic phenomena in the isosceles three-body problem

  • R. Moeckel
  • SIAM J. Math. Anal. 15
  • 1984
1 Excerpt

Homoclinic orbits and oscillations for the planar three-body problem

  • C. Robinson
  • J. Differential Equations 52
  • 1984
3 Excerpts

Parabolic orbits for the planar tree body problem

  • R. Easton
  • J. Differential Equations 52
  • 1984
2 Excerpts

Similar Papers

Loading similar papers…