The present work studies the robustness of certain basic homoclinic motions in an equilateral restricted four-body problem. The problem can be viewed as a two-parameter family of conservative autonomous vector fields. The main tools are numerical continuation techniques for homoclinic and periodic orbits, as well as formal series methods for computing normal forms and center stable/unstable manifold parameterizations. After careful numerical study of a number of special cases, we formulate several conjectures about the global bifurcations of the homoclinic families.
Bibliographical noteFunding Information:
The authors would like to thank J.B. van den Berg and Bob Rink for many helpful discussions and much encouragement as this work progressed. The authors owe sincere thanks to two anonymous referees who carefully read the submitted version of the manuscript, and made a number of insightful comments and corrections which improved the final printed version of the paper. W. Hetbrij was partially supported by NWO-VICI Grant 639033109. J.D. Mireles James was partially supported by NSF Grant DMS-1813501.
The first author was partially supported by NWO-VICI Grant 639033109.
© 2021, The Author(s), under exclusive licence to Springer Nature B.V. part of Springer Nature.
Copyright 2021 Elsevier B.V., All rights reserved.
- Center manifold parameterization
- Critical equilibria
- Four-body problem
- Homoclinic dynamics