On the free time minimizers of the NewtonianN-body problem

DOI10.1017/S0305004113000650zbMath1331.70035arXiv1301.7034MaRDI QIDQ5408697

Adriana da Luz, Ezequiel Maderna

Publication date: 11 April 2014

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.7034

zbMATH Keywords

existencedynamicsfree time minimizerspecial class of motionsstrong global minimization property

Mathematics Subject Classification ID

Variational principles in infinite-dimensional spaces (58E30) (n)-body problems (70F10) Nearly integrable Hamiltonian systems, KAM theory (70H08) Optimality conditions for free problems in one independent variable (49K05)

Related Items (16)

Free time minimizers for the three-body problem ⋮ Entire parabolic trajectories as minimal phase transitions ⋮ Parabolic solutions for the planar \(N\)-centre problem: multiplicity and scattering ⋮ An index theory for zero energy solutions of the planar anisotropic Kepler problem ⋮ An index theory for collision, parabolic and hyperbolic solutions of the Newtonian \(n\)-body problem ⋮ Null angular momentum and weak KAM solutions of the Newtonian \(N\)-body problem ⋮ Busemann functions for the \(N\)-body problem ⋮ An index theory for asymptotic motions under singular potentials ⋮ Entire minimal parabolic trajectories: the planar anisotropic Kepler problem ⋮ Viscosity solutions and hyperbolic motions: a new PDE method for the \(N\)-body problem ⋮ Minimizing configurations and Hamilton-Jacobi equations of homogeneous \(N\)-body problems ⋮ Scattering parabolic solutions for the spatial \(N\)-centre problem ⋮ Variational construction for heteroclinic orbits of the \(N\)-center problem ⋮ Minimal geodesics of the isosceles three body problem ⋮ Geodesic rays of the \(N\)-body problem ⋮ Translation invariance of weak KAM solutions of the Newtonian $N$-body problem

Cites Work

• Action minimizing invariant measures for positive definite Lagrangian systems
• Globally minimizing parabolic motions in the Newtonian \(N\)-body problem
• On the final evolution of the n-body problem
• Total collison, completely parabolic motions and homothety reduction in the \(n\)-body problem
• Connecting orbits between static classes for generic Lagrangian systems
• How the method of minimization of action avoids singularities
• On the existence of collisionless equivariant minimizers for the classical \(n\)-body problem
• Weak KAM theorem on non compact manifolds
• Translation invariance of weak KAM solutions of the Newtonian $N$-body problem
• On weak KAM theory for N-body problems
• A smooth pseudo-gradient for the Lagrangian action functional
• Lagrangian flows: The dynamics of globally minimizing orbits
• Action potential and weak KAM solutions

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