Oscillatory orbits in the restricted elliptic planar three body problem

Marcel Guardia; Tere M. Seara; Pau Martín; Lara Sabbagh

doi:10.3934/dcds.2017009

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2017, Volume 37, Issue 1: 229-256. Doi: 10.3934/dcds.2017009

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Oscillatory orbits in the restricted elliptic planar three body problem

1.
Departament de Matemàtiques, Universitat Politècnica de Catalunya, Diagonal 647, 08028 Barcelona, Spain
2.
Departament de Matemàtiques, Universitat Politècnica de Catalunya, Campus Nord, Edifici C3, C. Jordi Girona, 1-3, 08034 Barcelona, Spain
3.
Mathematics Institute, Zeeman Building, University of Warwick, Coventry CV4 7AL, United Kingdom

* Corresponding author: Marcel Guardia
* Corresponding author: Marcel Guardia

Received: March 2016

Revised: September 2016

Published online: January 2017

M.G., P. M. and T. S. are partially supported by the Spanish MINECO-FEDER Grant MTM2015-65715-P and the Catalan Grant 2014SGR504. T.S. is also supported by by the Russian Scientific Foundation grant 14-41-00044. and European Marie Curie Action FP7-PEOPLE-2012-IRSES: BREUDS L. S. is partially supported by the EPSRC grant EP/J003948/1

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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.

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Mathematics Subject Classification: Primary:70F15, 37J40.

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