Research Group:
Speaker:
Alberto Maspero
Institution:
SISSA
Schedule:
Monday, March 19, 2018 - 10:00
Location:
A-136
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.