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\(n\)-body problem and choreographies (Q6599399)

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scientific article; zbMATH DE number 7907938

Language	Label	Description	Also known as
English	\(n\)-body problem and choreographies	scientific article; zbMATH DE number 7907938

Statements

scholarly article

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\(n\)-body problem and choreographies (English)

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Susanna Terracini

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publication date

6 September 2024

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zbMATH Keywords

\(n\)-body problem

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celestial mechanics

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KAM theory

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perturbation theory

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MaRDI profile type

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Non-collision periodic solutions for a class of symmetric 3-body type problems

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Dual variational methods in critical point theory and applications

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Minimization properties of Hill's orbits and applications to some \(N\)-body problems

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A new branch of mountain pass solutions for the choreographical 3-body problem

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SMALL DENOMINATORS AND PROBLEMS OF STABILITY OF MOTION IN CLASSICAL AND CELESTIAL MECHANICS

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Periodic solutions of Hamiltonian systems of 3-body type

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Morse index properties of colliding solutions to the \(N\)-body problem

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Action minimizing orbits in the<i>n</i>-body problem with simple choreography constraint

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A bisection algorithm for the numerical mountain pass

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Symmetry groups of the planar three-body problem and action-minimizing trajectories

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On the Singularities of Generalized Solutions to n-Body-Type Problems

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Symmetries and noncollision closed orbits for planar N-body-type problems

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Elliptic two-dimensional invariant tori for the planetary three-body problem

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N-Dimensional Elliptic Invariant Tori for the Planar (N+1)-Body Problem

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Action-minimizing orbits in the parallelogram four-body problem with equal masses

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On Chenciner-Montgomery's orbit in the three-body problem.

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Binary decompositions for planar \(N\)-body problems and symmetric periodic solutions

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Variational methods on periodic and quasi-periodic solutions for the N-body problem

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Minima de l'intégrale d'action et équilibres relatifs de n corps

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The equation for the vertical variations of a relative equilibrium as a source of new periodic solutions of the \(N\) body problem.

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A remarkable periodic solution of the three-body problem in the case of equal masses

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Minima of the action integral in the Newtonian problem of 4 bodies with equal masses: `Hip-hop' orbits

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Rotating Eights: I. The three Γ<sub><b><i>i</i></b></sub>families

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Non-collision periodic solutions of the N-body system

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Collision orbits in the anisotropic Kepler problem

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Non regularizability of the anisotropic Kepler problem

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Triple collision in the planar isosceles three body problem

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Regularization of partial collisions in the \(N\)-body problem

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Painlevé's conjecture

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Near-collision dynamics for particle systems with quasihomogeneous potentials

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On the global dynamics of the anisotropic Manev problem

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The Kepler problem with anisotropic perturbations

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Central configurations and total collisions for quasihomogeneous \(n\)-body problems

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Collision Singularities in Celestial Mechanics

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Démonstration du ‘théorème d'Arnold’ sur la stabilité du système planétaire (d'après Herman)

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Symmetry groups and non-planar collisionless action-minimizing solutions of the three-body problem in three-dimensional space

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Transitive decomposition of symmetry groups for the \(n\)-body problem

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On the existence of collisionless equivariant minimizers for the classical \(n\)-body problem

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Conservative Dynamical Systems Involving Strong Forces

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A Minimizing Property of Keplerian Orbits

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Stability of the planetary three-body problem. I: Expansion of the planetary Hamiltonian

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Sur la régularisation du problème des trois corps.

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Periodic solutions to some problems of \(n\)-body type

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On the existence of infinitely many periodic solutions to some problems of <i>n</i>‐body type

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The family \(P_{12}\) of the three-body problem -- the simplest family of periodic orbits, with twelve symmetries per period

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How the method of minimization of action avoids singularities

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Triple collision in the collinear three-body problem

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Von Zeipel's theorem on singularities in celestial mechanics

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On central configurations

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The<b><i>N</i></b>-body problem, the braid group, and action-minimizing periodic solutions

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Braids in classical dynamics

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Central configurations of the N-body problem via equivariant Morse theory

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The principle of symmetric criticality

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Sur les solutions périodiques et le principe de la moindre action.

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Singularities of the n-body problem. I

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Study of the critical points at infinity arising from the failure of the Palais-Smale condition for 𝑛-body type problems

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Stability of the planetary three-body problem. II: KAM theory and existence of quasiperiodic motions

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Singularities and collisions of Newtonian gravitational systems

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Identifiers

zbMATH Open document ID

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10.1007/978-1-0716-2621-4_351

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:6599399

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