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Bounded orbits for three bodies in $ℝ^{4}$ $ℝ^{4}$

Alain Albouy

https://orcid.org/0000-0003-4286-4758

CNRS, Observatoire de Paris, 77, avenue Denfert-Rochereau, 75014 Paris, France

E-mail Address: alain.albouy@obspm.fr

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and

Holger R. Dullin

https://orcid.org/0000-0001-6617-196X

University of Sydney, School of Mathematics and Statistics, Sydney, NSW 2006, Australia

E-mail Address: holger.dullin@sydney.edu.au

Corresponding author.

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https://doi.org/10.1142/S2972458924500035Cited by:0 (Source: Crossref)

Abstract

We consider the Newtonian 3-body problem in dimension 4, and fix a value of the angular momentum which is compatible with this dimension. We show that the energy function cannot tend to its infimum on an unbounded sequence of states. Consequently the infimum of the energy is its minimum. This completes our previous work [A. Albouy and H. R. Dullin, Relative equilibria of the 3-body problem in $ℝ^{4}$ $ℝ^{4}$ , J. Geom. Mech. 12(3) (2020) 323–341] on the existence of Lyapunov stable relative periodic orbits in the 3-body problem in $ℝ^{4}$ $ℝ^{4}$ .

Keywords:

AMSC: 37N05, 70F10, 70F15, 70H33, 53D20

References

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2. A. Albouy and H. R. Dullin, Relative equilibria of the 3-body problem in $R^{4}$ $R^{4}$ , J. Geom. Mech. 12(3) (2020) 323–341. Google Scholar
3. H. R. Dullin and J. Scheurle, Symmetry reduction of the 3-body problem in $R^{4}$ $R^{4}$ , J. Geom. Mech. 12(3) (2020) 377–394. Google Scholar
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Vol. 01, No. 01

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History

Received 9 October 2023

Accepted 18 February 2024

Published: 20 April 2024

Keywords

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System Upgrade on Tue, May 28th, 2024 at 2am (EDT)

Bounded orbits for three bodies in $ℝ^{4}$ $ℝ^{4}$

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Bounded orbits for three bodies in R4ℝ4<math altimg="eq-00001.gif" display="inline"><msup><mrow><mi>ℝ</mi></mrow><mrow><mn>4</mn></mrow></msup></math>

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