Platonic polyhedra, periodic orbits and chaotic motions in the \(N\)-body problem with non-Newtonian forces

DOI10.1007/s10884-014-9401-2zbMath1305.70024OpenAlexW2000841238MaRDI QIDQ487937

Giorgio Fusco, Giovanni Federico Gronchi

Publication date: 23 January 2015

Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10884-014-9401-2

zbMATH Keywords

variational methodsperiodic orbit\(N\)-body problemchaotic motions

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Equilibria and periodic trajectories for nonlinear problems in mechanics (70K42) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) (n)-body problems (70F10) Symmetry properties of polytopes (52B15) Existence theories in calculus of variations and optimal control (49J99)

Related Items

Symmetric constellations of satellites moving around a central body of large mass ⋮ Avoiding collisions under topological constraints in variational problems coming from celestial mechanics

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Platonic polyhedra, topological constraints and periodic solutions of the classical \(N\)-body problem
• Symmetric trajectories for the \(2N\)-body problem with equal masses
• Binary decompositions for planar \(N\)-body problems and symmetric periodic solutions
• On the existence of collisionless equivariant minimizers for the classical \(n\)-body problem
• Transitive decomposition of symmetry groups for the \(n\)-body problem
• Une caractérisation variationnelle des solutions de Lagrange du problème plan des trois corps
• On the Singularities of Generalized Solutions to n-Body-Type Problems
• TheN-body problem, the braid group, and action-minimizing periodic solutions
• Minima of the action integral in the Newtonian problem of 4 bodies with equal masses: `Hip-hop' orbits

This page was built for publication: Platonic polyhedra, periodic orbits and chaotic motions in the \(N\)-body problem with non-Newtonian forces