|
This article is cited in 2 scientific papers (total in 2 papers)
Algebraic Integrability and Geometry of the $\mathfrak{d}_3^{(2)}$ Toda Lattice
Djagwa Dehainsalaab a Laboratoire de Mathématiques et Applications, UMR CNRS 6086, France
b Université de Poitiers, Téléport 2,
Boulevard Marie et Pierre Curie, BP 30179, 86962 Futuroscope Chasseneuil Cedex, France
Abstract:
In this paper, we consider the Toda lattice associated to the twisted
affine Lie algebra $\mathfrak{d}_3^{(2)}$. We show that the generic fiber
of the momentum map of this system is an affine part of an Abelian surface
and that the flows of integrable vector fields are linear on this surface,
so that the system is algebraic completely integrable. We also give a
detailed geometric description of these Abelian surfaces and of the
divisor at infinity. As an application, we show that the lattice is
related to the Mumford system and we construct an explicit morphism
between these systems, leading to a new Poisson structure for the Mumford
system. Finally, we give a new Lax equation with spectral parameter for
this Toda lattice and we construct an explicit linearization of the
system.
Keywords:
Toda lattice, integrable systems, algebraic integrability, Abelian surface.
Received: 15.12.2009 Accepted: 21.08.2010
Citation:
Djagwa Dehainsala, “Algebraic Integrability and Geometry of the $\mathfrak{d}_3^{(2)}$ Toda Lattice”, Regul. Chaotic Dyn., 16:3-4 (2011), 330–355
Linking options:
https://www.mathnet.ru/eng/rcd441 https://www.mathnet.ru/eng/rcd/v16/i3/p330
|
Statistics & downloads: |
Abstract page: | 76 |
|