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A Bifurcation in the Family of Periodic Orbits for the Spatial Isosceles 3 Body Problem

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Abstract

In this paper we describe a 1-dimensional family of initial conditions \(\Sigma \) that provides reduced periodic solutions of the spatial isosceles 3-body problem. This family \(\Sigma \) contains a bifurcation point that make it look like the union of two embedded smooth curves. We will explain how the trajectories of the bodies in the solutions coming from one of the embedded curves have two symmetries while those coming from the other embedded curve only have one symmetry. We give an explanation for the existence of this bifurcation point.

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Acknowledgements

Funding was provided by AAUP Research Grant.

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  1. Central Connecticut State University, 123 Marcus White, 1615 Stanley Street, New Britain, CT, 06050, USA

    Oscar M. Perdomo

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  1. Oscar M. Perdomo
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Correspondence to Oscar M. Perdomo.

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Perdomo, O.M. A Bifurcation in the Family of Periodic Orbits for the Spatial Isosceles 3 Body Problem. Qual. Theory Dyn. Syst. 17, 411–428 (2018). https://doi.org/10.1007/s12346-017-0244-1

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