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- Title
Spatial periodic orbits in the equilateral circular restricted four-body problem: computer-assisted proofs of existence.
- Authors
Burgos-García, Jaime; Lessard, Jean-Philippe; James, J. D. Mireles
- Abstract
We use validated numerical methods to prove the existence of spatial periodic orbits in the equilateral restricted four-body problem. We study each of the vertical Lyapunov families (up to symmetry) in the triple Copenhagen problem, as well as some halo and axial families bifurcating from planar Lyapunov families. We consider the system with both equal and non-equal masses. Our method is constructive and non-perturbative, being based on a posteriori analysis of a certain nonlinear operator equation in the neighborhood of a suitable approximate solution. The approximation is via piecewise Chebyshev series with coefficients in a Banach space of rapidly decaying sequences. As by-product of the proof, we obtain useful quantitative information about the location and regularity of the solution.
- Subjects
NONLINEAR operator equations; CHEBYSHEV series; BANACH spaces; MATHEMATICAL physics; KEPLER problem
- Publication
Celestial Mechanics & Dynamical Astronomy, 2019, Vol 131, Issue 1, p1
- ISSN
0923-2958
- Publication type
Article
- DOI
10.1007/s10569-018-9879-8