Título:
Viscosity solutions and hyperbolic motions : a new PDE method for the N-body problem
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Autor:
Maderna, Ezequiel
Venturelli, Andrea
Venturelli, Andrea
Tutor:
Tipo de documento:
Artículo
Editor:
Palabras clave:
N-body problem
Hamilton-Jacobi equation
Viscosity solutions
Hamilton-Jacobi equation
Viscosity solutions
Descriptores:
Año de publicación:
2020
Contenido:
Resumen:
We prove for the N-body problem the existence of hyperbolic motions for any prescribed limit shape and any given initial configuration of the bodies. The energy level h>0 of the motion can also be chosen arbitrarily. Our approach is based on the construction of global viscosity solutions for the Hamilton-Jacobi equation H(x,dxu)=h. We prove that these solutions are fixed points of the associated Lax-Oleinik semigroup. The presented results can also be viewed as a new application of Marchal’s Theorem, whose main use in recent literature has been to prove the existence of periodic orbits.
Descripción:
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Editorial:
Princeton University
EN:
Annals of Mathematics, vol. 192, no. 2, 2020, pp. 499-550.
Financiadores:
MATH AmSud Sidiham, CSIC grupo 618 e IFUM LIA-CNRS.
Citación:
Maderna, E. y Venturelli, A. "Viscosity solutions and hyperbolic motions : a new PDE method for the N-body problem". Annals of Mathematics. [en línea]. 2020, vol. 192, no. 2, pp. 499-550. DOI: 10.4007/annals.2020.192.2.5.
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ISSN:
0003-486X
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Licencia:
Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)
Colecciones:
| Ficheros | Descripción | Tamaño | Formato | ||
|---|---|---|---|---|---|
| MV20.pdf | Preprint | 720.26 KB | Adobe PDF |