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6 papers · 1 filter
Saari's Homographic Conjecture of the Three-Body Problem
Florin Diacu, Toshiaki Fujiwara, Ernesto Perez-Chavela +1
Saari's homographic conjecture, which extends a classical statement proposed by Donald Saari in 1970, claims that solutions of the Newtonian -body problem with constant configur…
Central Configurations and Total Collisions for Quasihomogeneous n-Body Problems
Florin Diacu, Ernesto Perez-Chavela, Manuele Santoprete
We consider -body problems given by potentials of the form with constants, . To analyze the dynamics of the problem, we first pro…
Saari's Conjecture for the Collinear -Body Problem
Florin Diacu, Ernesto Perez-Chavela, Manuele Santoprete
In 1970 Don Saari conjectured that the only solutions of the Newtonian -body problem that have constant moment of inertia are the relative equilibria. We prove this conjecture i…
The Kepler Problem with Anisotropic Perturbations
Florin Diacu, Ernesto Perez-Chavela, Manuele Santoprete
We study a 2-body problem given by the sum of the Newtonian potential and an anisotropic perturbation that is a homogeneous function of degree , . For , the sets o…
Computing with almost periodic functions
R. V. Moody, M. Nesterenko, J. Patera
The paper develops a method for discrete computational Fourier analysis of functions defined on quasicrystals and other almost periodic sets. A key point is to build the analysis a…
Orthogonality within the Families of C-, S-, and E-Functions of Any Compact Semisimple Lie Group
Robert V. Moody, Jiri Patera
The paper is about methods of discrete Fourier analysis in the context of Weyl group symmetry. Three families of class functions are defined on the maximal torus of each compact si…