Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Oscillatory orbits in the restricted elliptic planar three body problem

Pages: 229 - 256, Volume 37, Issue 1, January 2017      doi:10.3934/dcds.2017009

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Marcel Guardia - Departament de Matematiques, Universitat Politecnica de Catalunya, Diagonal 647, 08028 Barcelona, Spain (email)
Tere M. Seara - Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya, Av. Diagonal, 647, 08028 Barcelona, Spain (email)
Pau Martín - Departament de Matemàtiques, Universitat Politècnica de Catalunya, Campus Nord, Edifici C3, C. Jordi Girona, 1-3, 08034 Barcelona, Spain (email)
Lara Sabbagh - Mathematics Institute, Zeeman Building, University of Warwick, Coventry CV4 7AL, United Kingdom (email)

Abstract: The restricted planar elliptic three body problem models the motion of a massless body under the Newtonian gravitational force of two other bodies, the primaries, which evolve in Keplerian ellipses.
    A trajectory is called oscillatory if it leaves every bounded region but returns infinitely often to some fixed bounded region. We prove the existence of such type of trajectories for any values for the masses of the primaries provided the eccentricity of the Keplerian ellipses is small.

Keywords:  Restricted three body problem, final motions, oscillatory motions, parabolic points, lambda lemma.
Mathematics Subject Classification:  Primary: 70F15, 37J40.

Received: March 2016;      Revised: September 2016;      Available Online: November 2016.