American Institute of Mathematical Sciences

March  2019, 24(3): 1007-1020. doi: 10.3934/dcdsb.2019003

Periodic orbits for the perturbed planar circular restricted 3–body problem

 1 Nonlinear Analysis and Applied Mathematics Research Group (NAAM), Mathematics Department, King Abdulaziz University, Jeddah, Saudi Arabia 2 Celestial Mechanics Unit, Astronomy Department, National Research Institute of Astronomy and Geophysics (NRIAG), Helwan 11421, Cairo, Egypt 3 Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Hospital de Marina, 30203-Cartagena, Región de Murcia, Spain 4 Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain

Received  July 2017 Revised  February 2018 Published  March 2019 Early access  January 2019

Fund Project: We thank to both reviewers their comments and suggestions that help us to improve this paper. The first and second author of this work were partially supported by MINECO grant number MTM2014-51891-P and Fundación Séneca de la Región de Murcia grant number 19219/PI/14. The first and third author are partially supported by a MINECO-FEDER grant MTM2016-77278-P, a MINECO grant MTM2013-40998-P, and an AGAUR grant number 2014SGR-568.

We characterize when the classical first and second kind of periodic orbits of the planar circular restricted $3$–body problem obtained by Poincaré, can be extended to perturbed planar circular restricted $3$–body problems. We put special emphasis when the perturbed forces are due to zonal harmonic or to a solar sail.

Citation: Elbaz I. Abouelmagd, Juan Luis García Guirao, Jaume Llibre. Periodic orbits for the perturbed planar circular restricted 3–body problem. Discrete & Continuous Dynamical Systems - B, 2019, 24 (3) : 1007-1020. doi: 10.3934/dcdsb.2019003
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