On weak KAM theory for N-body problems

DOI10.1017/S0143385711000046zbMath1257.37039arXiv1502.06273MaRDI QIDQ2908169

Ezequiel Maderna

Publication date: 4 September 2012

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1502.06273

zbMATH Keywords

KAM theory\(N\)-body problemviscosity solutionsHamilton-Jacobi

Mathematics Subject Classification ID

Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Hamilton-Jacobi equations in mechanics (70H20) (n)-body problems (70F10)

Related Items (13)

Free time minimizers for the three-body problem ⋮ Entire parabolic trajectories as minimal phase transitions ⋮ Null angular momentum and weak KAM solutions of the Newtonian \(N\)-body problem ⋮ Busemann functions for the \(N\)-body problem ⋮ Existence of hyperbolic motions to a class of Hamiltonians and generalized \(N\)-body system via a geometric approach ⋮ 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 ⋮ On the free time minimizers of the NewtonianN-body problem ⋮ A minimizing property of hyperbolic Keplerian orbits ⋮ Geodesic rays of the \(N\)-body problem ⋮ Translation invariance of weak KAM solutions of the Newtonian $N$-body problem ⋮ Globally minimizing parabolic motions in the Newtonian \(N\)-body problem

Cites Work

• Unnamed Item
• Globally minimizing parabolic motions in the Newtonian \(N\)-body problem
• Lagrangian graphs, minimizing measures and Mañé's critical values
• 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
• Théorème KAM faible et théorie de Mather sur les systèmes lagrangiens
• Invariance of global solutions of the Hamilton-Jacobi equation
• A remarkable periodic solution of the three-body problem in the case of equal masses
• Action potential and weak KAM solutions

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