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Birkhoff coordinates for the Toda lattice in the limit of infinitely many particles with an application to FPU

Alberto Maspero
Institution: 
SISSA
Location: 
A-136
Schedule: 
Monday, March 19, 2018 - 10:00
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 $\tfrac{R'}{N^a}$  (in discrete Sobolev-analytic norms) into a ball of radius $\tfrac{R'}{N^a}$ with  (with $R$, $R'$ independent of $N$) if and only if $a \geq 2$. The proof of the theorem is based on a new quantitative version of a Vey type theorem by Kuksin and Perelman.This is a joint work with Dario Bambusi. 

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