Classification of positive elliptic-elliptic rotopulsators on Clifford tori

DOI10.1016/J.JMAA.2023.127154zbMath1526.70012arXiv2011.14539OpenAlexW3109655633MaRDI QIDQ6155819

Pieter Tibboel

Publication date: 7 June 2023

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2011.14539

zbMATH Keywords

regular polygoncurved \(n\)-body problemconstant Gaussian curvature spaceelliptic-elliptic rotopulsator positiveness criterion

Mathematics Subject Classification ID

Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) (n)-body problems (70F10)

Cites Work

• Finiteness of polygonal relative equilibria for generalised quasi-homogeneous \(n\)-body problems and \(n\)-body problems in spaces of constant curvature
• The curved \(N\)-body problem: risks and rewards
• Existence of a lower bound for the distance between point masses of relative equilibria in spaces of constant curvature
• Relative equilibria of the curved \(N\)-body problem.
• The \(n\)-body problem in spaces of constant curvature. II: Singularities
• Existence of a class of rotopulsators
• The restricted two-body problem in constant curvature spaces
• Kepler's problem in constant curvature spaces
• Central configurations of the curved \(N\)-body problem
• Stability of fixed points and associated relative equilibria of the 3-body problem on \({\mathbb {S}}^1\) and \({\mathbb {S}}^2\)
• Two-body problem on a sphere. Reduction, stochasticity, periodic orbits
• Continuation of relative equilibria in the \(n\)-body problem to spaces of constant curvature
• Hyperbolic relative equilibria for the negative curved \(n\)-body problem
• Variational property of periodic Kepler orbits in constant curvature spaces
• Circular non-collision orbits for a large class of \(n\)-body problems
• Bifurcation of relative equilibria for vortices and general homogeneous potentials
• Rotopulsators of the curved \(N\)-body problem
• Computing Planar and Spherical Choreographies
• An intrinsic approach in the curved $n$-body problem. The positive curvature case
• All the Lagrangian relative equilibria of the curved 3-body problem have equal masses
• Three-dimensional central configurations in ℍ3 and 𝕊3
• On the singularities of the curved $n$-body problem
• Eulerian relative equilibria of the curved 3-body problems in 𝐒²
• Central potentials on spaces of constant curvature: The Kepler problem on the two-dimensional sphere S2 and the hyperbolic plane H2
• Polygonal rotopulsators of the curved n-body problem
• Polygonal homographic orbits in spaces of constant curvature
• The non-existence of centre-of-mass and linear-momentum integrals in the curved N-body problem
• The Classical N-body Problem in the Context of Curved Space
• Results on equality of masses for choreographic solutions of n-body problems
• Rectangular orbits of the curved 4-body problem
• Existence of a lower bound for the distance between point masses of relative equilibria for generalised quasi-homogeneous n-body problems and the curved n-body problem
• Polygonal homographic orbits of the curved $n$-body problem

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