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arXiv · 1105.4484

Translation Invariance of weak KAM solutions of the Newtonian N-body problem

Ezequiel Maderna
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Abstract

We consider in this note the Hamilton-Jacobi equation H(x, dx u) = c, where c \geq 0, of the classical N-body problem in an Euclidean space E of dimension k \geq 2. The fixed points of the Lax-Oleinik semigroup are global viscosity solutions for the critical value of the constant (c = 0) also called weak KAM solutions. We show that all these solutions are invariant under the action of E by translations on the space of configurations. We deduce the existence of non-invariant solutions for the super-critical equations (c > 0).

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Ezequiel Maderna. 2011-05-23. Translation Invariance of weak KAM solutions of the Newtonian N-body problem. https://doi.org/10.1090/s0002-9939-2013-11542-x

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