Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4589793 | Journal of Functional Analysis | 2016 | 70 Pages |
Abstract
In this paper we study the Birkhoff coordinates (Cartesian action angle coordinates) of the Toda lattice with periodic boundary condition in the limit where the number N of the particles tends to infinity. We prove that the transformation introducing such coordinates maps analytically a complex ball of radius R/NαR/Nα (in discrete Sobolev-analytic norms) into a ball of radius R′/NαR′/Nα (with R,R′>0R,R′>0 independent of N ) if and only if α≥2α≥2. Then we consider the problem of equipartition of energy in the spirit of Fermi–Pasta–Ulam. We deduce that corresponding to initial data of size R/N2R/N2, 0
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Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
D. Bambusi, A. Maspero,