Symmetries of the periodic Toda lattice, with an application to normal forms and perturbations of the lattice with Dirichlet boundary conditions

2013/12/19 by Henrici, Andreas
#37J15 #37J40 #37K05 #70H08 #70H33 #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1312.5612

Abstract

Symmetries of the periodic Toda lattice are expresssed in action-angle coordinates and characterized in terms of the periodic and Dirichlet spectrum of the associated Jacobi matrices. Using these symmetries, the phase space of the lattice with Dirichlet boundary conditions is embedded into the phase space of a higher-dimensional periodic lattice. As an application, we obtain a Birkhoff normal form and a KAM theorem for the lattice with Dirichlet boundary conditions.

Related

• Birkhoff normal form for the periodic Toda lattice
• The periodic and open Toda lattice
• Global action-angle variables for the periodic Toda lattice
• The Toda lattice, old and new
• Solutions of the periodic Toda lattice via the projection procedure and by the algebra-geometric method