牛顿N体问题弱KAM解的平移不变性
Translation Invariance of weak KAM solutions of the Newtonian N-body problem
摘要：
本文考虑k维\geq 2欧几里得空间E中经典N体问题的Hamilton-Jacobi方程H（x，dx u）= c，其中c \geq 0. Lax-Oleinik半群的不动点是常数（c = 0）的临界值的整体黏性解，也称为弱KAM解.我们表明，所有这些解决方案是不变的作用下，E的平移空间的配置。我们证明了超临界方程（c > 0）非不变解的存在性。
英文摘要：
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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