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Эта публикация цитируется в 2 научных статьях (всего в 2 статьях)
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
Аннотация:
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.
Ключевые слова:
Toda lattice, integrable systems, algebraic integrability, Abelian surface.
Поступила в редакцию: 15.12.2009 Принята в печать: 21.08.2010
Образец цитирования:
Djagwa Dehainsala, “Algebraic Integrability and Geometry of the $\mathfrak{d}_3^{(2)}$ Toda Lattice”, Regul. Chaotic Dyn., 16:3-4 (2011), 330–355
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd441 https://www.mathnet.ru/rus/rcd/v16/i3/p330
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