Data di Pubblicazione:
2014
Citazione:
BIRKHOFF COORDINATES OF INTEGRABLE HAMILTONIAN SYSTEMS IN ASYMPTOTIC REGIMES / A. Maspero ; tutor: D. Bambusi, T. Kappeler ; coordinator: L. Van Geemen. Università degli Studi di Milano, 2014 Dec 22. 26. ciclo, Anno Accademico 2013. [10.13130/maspero-alberto_phd2014-12-22].
Abstract:
In this thesis we investigate two examples of infinite dimensional integrable Hamiltonian systems in $1$-space dimension: the Toda chain with periodic boundary conditions and large number of particles, and the Korteweg-de Vries (KdV) equation on $\R$.
In the first part of the thesis 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 $R/N^\alpha$
(in discrete Sobolev-analytic norms) into a ball of radius $R'/N^\alpha$ (with $R,R'>0$ independent of $N$) if and only if
$\alpha\geq2$. 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 $R/N^2$, $0
Tipologia IRIS:
Tesi di dottorato
Keywords:
integrability; Birkhoff coordinates; Toda; KdV; scattering; FPU
Elenco autori:
A. Maspero
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