Critical homoclinics in a restricted four-body problem: numerical continuation and center manifold computations

Wouter Hetebrij; J. D. Mireles James

doi:10.1007/s10569-021-10002-2

Critical homoclinics in a restricted four-body problem: numerical continuation and center manifold computations

Wouter Hetebrij, J. D. Mireles James^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to Journal › Article › Academic › peer-review

Abstract

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.

Original language	English
Article number	5
Pages (from-to)	1-48
Number of pages	48
Journal	Celestial Mechanics and Dynamical Astronomy
Volume	133
Issue number	2
Early online date	15 Feb 2021
DOIs	https://doi.org/10.1007/s10569-021-10002-2
Publication status	Published - Feb 2021

Bibliographical note

Funding 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.

Funding Information:
The first author was partially supported by NWO-VICI Grant 639033109.

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Nature B.V. part of Springer Nature.

Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.

Funding

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.

Funders	Funder number
NWO-VICI	639033109
National Science Foundation	DMS-1813501
Directorate for Mathematical and Physical Sciences	1813501

Keywords

Center manifold parameterization
Critical equilibria
Four-body problem
Homoclinic dynamics

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abstract = "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.",

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Critical homoclinics in a restricted four-body problem: numerical continuation and center manifold computations

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Keywords

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