Extended integrability and bi-Hamiltonian systems
type: Item
instance of: scholarly article
title: Extended integrability and bi-Hamiltonian systems
zbMATH Open document ID: 0931.37028
published in: Communications in Mathematical Physics
publication date: 2000-03-07T00:00:00Z
review text: The paper deals with the problem of integrability of Hamiltonian systems. The author presents an extension of the Liouville integrability which allows him among other interesting cases, to treat the dynamics of an electron on the torus \(T^2\subset \mathbb{R}^3\) in an electromagnetic field and to prove that the corresponding Hamiltonian system on \(T^*(T^2)\) is bi-Hamiltonian and integrable in an extended sense. The main result consists of the complete classification of all \(\frac{k(k+1)} {2}\) nonequivalent canonical forms of integrable Hamiltonian systems and invariant symplectic structures.
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 37G35
zbMATH DE Number: 1203794
zbMATH Keywords: integrability
zbMATH Keywords: Hamiltonian systems
zbMATH Keywords: Liouville integrability
zbMATH Keywords: Hamiltonian system
zbMATH Keywords: symplectic structures
author: Oleg I. Bogoyavlenskij
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: s002200050412
OpenAlex ID: W2010422757
DOI: 10.1007/S002200050412
description: scientific article; zbMATH DE number 1203794