On Coxeter-Toda lattices

Author(s)

Eber Daniel Chuño Vizarreta

• Document type: Doctoral Thesis
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB)
• Defense date: 2016-03-29

Examining board members

Igor Mencattini; Daniel Smania Brandão; Alejandro Cabrera; Frank Michael Forger; Marcos Benevenuto Jardim

• Advisor: Igor Mencattini; Carlos Henrique Grossi Ferreira

Abstract

This work aims to study the bi-Hamiltonian structure of a class of dynamical systems. After introducing the relevant tools, namely the notions of Poisson manifold, Poisson-Lie group and of network dened in a disc and in an annulus, we will introduce the dynamical systems of interest for this dissertation, i.e., the Coxeter-Toda lattices. These dynamical systems, whose phase-space can be identied with a suitable quotient of a Coxeter double Bruhat cell of the general linear group, are obtained by reduction starting from the Toda ow on GLn. In the nal part of the present work will be presented some results concerning a discrete integrable system close to the so called Pentagram map, which is a discretization of the Boussinesq dynamical system.. (AU)

• FAPESP's process: 12/04707-9 - Clusters Algebras and Integrable Systems
• Grantee: Eber Daniel Chuno Vizarreta
• Support Opportunities: Scholarships in Brazil - Doctorate