Algebraic integrability of the Toda lattice \({\mathfrak d}^{(2)}_3\)
type: Item
instance of: scholarly article
title: Algebraic integrability of the Toda lattice \({\mathfrak d}^{(2)}_3\)
zbMATH Open document ID: 1211.37053
author: Djagwa Dehainsala
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2009-12-22T00:00:00Z
review text: This paper studies the algebraic integrability of the Toda lattice associated with the affine Lie algebra \(\mathfrak{d}_{3}^{(2)}\). This is a polynomial dynamical system in a hyperplane of dimension 5 in \({\mathbb C}^{6}\) admitting 3 integrals of polynomial form. Using the Painlev'e divisors it is shown that this system is an algebraically integrable system. Furthermore a morphism between this system and the Mumford system is established.
Mathematics Subject Classification ID: 37F10
Mathematics Subject Classification ID: 14H70
Mathematics Subject Classification ID: 37K10
zbMATH DE Number: 5651247
zbMATH Keywords: algebraic integrabiliy
zbMATH Keywords: Toda lattice
reviewed by: Athanasios Yannacopoulos
MaRDI profile type: Publication
full work available at URL: j.crma.2009.09.013
OpenAlex ID: W2008144198
cites work: The complex geometry of the Kowalewski-Painlevé analysis
cites work: Q4650506
cites work: Tata lectures on theta. II: Jacobian theta functions and differential equations. With the collaboration of C. Musili, M. Nori, E. Previato, M. Stillman, and H. Umemura
cites work: Integrable systems in the realm of algebraic geometry.
DOI: 10.1016/J.CRMA.2009.09.013
description: scientific article; zbMATH DE number 5651247