Saari's Conjecture for Elliptical Motions and Minimizing Solutions of the N-body Problem
DOI10.1137/140987663zbMath1348.70027OpenAlexW2286328182WikidataQ123343616 ScholiaQ123343616MaRDI QIDQ5744674
Publication date: 19 February 2016
Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/140987663
periodic solutionsvariational methodsFourier coefficientscelestial mechanics\(n\)-body problemsspecial Fourier seriesFourier series of functions with special properties
Periodic solutions to ordinary differential equations (34C25) Variational methods for problems in mechanics (70G75) Celestial mechanics (70F15) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16) (n)-body problems (70F10)
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Cites Work
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- Finiteness of relative equilibria of the four-body problem
- Saari's conjecture for the restricted three-body problem
- A proof of Saari's conjecture for the three-body problem in R\(^d\)
- The \(n\)-body problem and mutual distances
- Binary decompositions for planar \(N\)-body problems and symmetric periodic solutions
- Nonplanar and noncollision periodic solutions for \(N\)-body problems
- Mathematical problems for the next century
- New periodic solutions for 3-body problems
- Saari's conjecture for the planar three-body problem with equal masses
- A counterexample to a generalized Saari's conjecture with a continuum of central configurations
- On central configurations
- On the existence of collisionless equivariant minimizers for the classical \(n\)-body problem
- Existence and minimizing properties of retrograde orbits to the three-body problem with various choices of masses
- Mathematical aspects of classical and celestial mechanics. Transl. from the Russian by E. Khukhro.
- Variational methods for the choreography solution to the three-body problem
- Saari’s homographic conjecture for a planar equal-mass three-body problem under a strong force potential
- Saari’s homographic conjecture for a planar equal-mass three-body problem under the Newton gravity
- Saari's conjecture is true for generic vector fields
- Saari's homographic conjecture of the three-body problem
- Minima de l'intégrale d'action et équilibres relatifs de n corps
- Action minimizing orbits in then-body problem with simple choreography constraint
- A computer-assisted proof of Saari’s conjecture for the planar three-body problem
- Saari’s conjecture for the collinear $n$-body problem
- Some counterexamples to a generalized Saari’s conjecture
- Mathematical analysis II. Transl. from the 4th Russian edition by Roger Cooke
- Geometric characterizations for variational minimization solutions of the 3-body problem
- Minima of the action integral in the Newtonian problem of 4 bodies with equal masses: `Hip-hop' orbits
- A remarkable periodic solution of the three-body problem in the case of equal masses
- Action-minimizing orbits in the parallelogram four-body problem with equal masses
- A minimizing property of Lagrangian solutions