Integrable symplectic maps
type: Item
instance of: scholarly article
title: Integrable symplectic maps
zbMATH Open document ID: 0734.58023
DOI: 10.1016/0167-2789(91)90149-4
author: N. E. Zubov
published in: Physica D
publication date: 1991-01-01T00:00:00Z
review text: The paper first reviews the concept of a symplectic map, its characterization and properties and various ways of construction. Among these is a rather formal discrete version of Euler-Lagrange equations, which relates to earlier work by Maeda on discrete Hamiltonian and Lagrangian systems. Integrability of a symplectic map essentially means linearizability, and an analogue of the Arnold-Liouville theorem states that such integrability follows from the existence of a sufficient number of independent invariants in involution. The second part of the paper shows how integrable symplectic maps can be obtained from stationary solutions of discrete versions of known integrable evolution equations, such as the non-linear Schrödinger equation and the KdV equation.
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 35Q53
zbMATH DE Number: 4214984
zbMATH Keywords: complete integrability
zbMATH Keywords: symplectic map
reviewed by: W. Sarlet
MaRDI profile type: Publication
full work available at URL: 0167-2789(91)90149-4
OpenAlex ID: W2094760001
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description: scientific article; zbMATH DE number 4214984