Viscosity solutions and hyperbolic motions : a new PDE method for the N-body problem
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.
| 2020 | |
| MATH AmSud Sidiham, CSIC grupo 618 e IFUM LIA-CNRS. | |
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N-body problem Hamilton-Jacobi equation Viscosity solutions |
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| Inglés | |
| Universidad de la República | |
| COLIBRI | |
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https://annals.math.princeton.edu/2020/192-2/p05
https://hdl.handle.net/20.500.12008/36121 |
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| Acceso abierto | |
| Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| Sumario: | 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. |
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