A new branch of mountain pass solutions for the choreographical 3-body problem
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Publication:996030
DOI10.1007/s00220-006-0111-4zbMath1118.70008OpenAlexW2077226602MaRDI QIDQ996030
Gianni Arioli, Vivina Barutello, Susanna Terracini
Publication date: 11 September 2007
Published in: Communications in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00220-006-0111-4
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Cites Work
- Unnamed Item
- Unnamed Item
- Computer-assisted methods for the study of stationary solutions in dissipative systems, applied to the Kuramoto-Sivashinski equation
- The principle of symmetric criticality
- Symmetry groups of the planar three-body problem and action-minimizing trajectories
- A mountain pass method for the numerical solution of semilinear wave equations
- A renormalization group fixed point associated with the breakup of golden invariant tori
- On the existence of collisionless equivariant minimizers for the classical \(n\)-body problem
- Dual variational methods in critical point theory and applications
- A bisection algorithm for the numerical mountain pass
- Two novel methods and multi-mode periodic solutions for the Fermi-Pasta-Ulam model
- Existence of a third solution for a class of B.V.P. with jumping nonlinearities
- A Geometric Description of the Neighbourhood of a Critical Point Given by the Mountain-Pass Theorem
- The Structure of the Critical Set in the Mountain Pass Theorem
- Nontrivial solutions of operator equations and Morse indices of critical points of min-max type
- Minima de l'intégrale d'action et équilibres relatifs de n corps
- The existence of simple choreographies for theN-body problem—a computer-assisted proof
- Action minimizing orbits in then-body problem with simple choreography constraint
- A mountain pass method for the numerical solution of semilinear elliptic problems
- A remarkable periodic solution of the three-body problem in the case of equal masses
- The family \(P_{12}\) of the three-body problem -- the simplest family of periodic orbits, with twelve symmetries per period
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