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Pré-Publication, Document De Travail Année : 2023

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

Résumé

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 \cite{AD19} on the existence of Lyapunov stable relative periodic orbits in the 3-body problem in ℝ4.

Dates et versions

hal-04284655 , version 1 (14-11-2023)

Identifiants

Citer

Alain Albouy, Holger R. Dullin. Bounded orbits for three bodies in $\mathbb{R}^4$. 2023. ⟨hal-04284655⟩
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