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- W3009199095 abstract "<p style='text-indent:20px;'>The 3-body problem in <inline-formula><tex-math id=M2>begin{document}$ mathbb{R}^4 $end{document}</tex-math></inline-formula> has 24 dimensions and is invariant under translations and rotations. We do the full symplectic symmetry reduction and obtain a reduced Hamiltonian in local symplectic coordinates on a reduced phase space with 8 dimensions. The Hamiltonian depends on two parameters <inline-formula><tex-math id=M3>begin{document}$ mu_1 > mu_2 ge 0 $end{document}</tex-math></inline-formula>, related to the conserved angular momentum. The limit <inline-formula><tex-math id=M4>begin{document}$ mu_2 to 0 $end{document}</tex-math></inline-formula> corresponds to the 3-dimensional limit. We show that the reduced Hamiltonian has three relative equilibria that are local minima and hence Lyapunov stable when <inline-formula><tex-math id=M5>begin{document}$ mu_2 $end{document}</tex-math></inline-formula> is sufficiently small. This proves the existence of balls of initial conditions of full dimension that do not contain any orbits that are unbounded." @default.
- W3009199095 created "2020-03-13" @default.
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- W3009199095 date "2020-01-01" @default.
- W3009199095 modified "2023-09-25" @default.
- W3009199095 title "Symmetry reduction of the 3-body problem in <inline-formula><tex-math id=M1>begin{document}$ mathbb{R}^4 $end{document}</tex-math></inline-formula>" @default.
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- W3009199095 doi "https://doi.org/10.3934/jgm.2020011" @default.
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