What is it about?
We have proved that the periodic orbits of first kind can be extended from the planar circular restricted 3-body problem to a perturbed planar circular restricted 3-body problem if this perturbed problem has a fi rst integral. It is an open problem to know when these periodic orbits can be extended if the perturbed problem has not a first integral. We also have shown that the periodic orbits of second kind can be extended from the planar circular restricted 3-body problem to a perturbed planar circular restricted 3-body problem
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Why is it important?
It is an open problem to know when these periodic orbits can be extended if the perturbed problem has not a first integral.
Perspectives
Our objective in the present work is to analyze when the first and second kind of periodic orbits found by Poincare in the planar circular restricted 3-body problem can be or not extended to periodic orbits of the perturbed planar circular restricted 3{body problem.
Prof. Elbaz I. Abouelmagd
National Research Institute of Astronomy and Geophysics (NRIAG)
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This page is a summary of: Periodic orbits for the perturbed planar circular restricted 3–body problem, Discrete and Continuous Dynamical Systems - B, January 2019, American Institute of Mathematical Sciences (AIMS),
DOI: 10.3934/dcdsb.2019003.
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