A hierarchy of multidimensional Hénon-Heiles systems
type: Item
instance of: scholarly article
title: A hierarchy of multidimensional Hénon-Heiles systems
zbMATH Open document ID: 1065.37054
author: Yun-Bo Zeng
publication date: 2000-01-01T00:00:00Z
review text: The original Hénon-Heiles system is described by a classical Hamiltonian with two degrees of freedom. The potential is a polynom of third order containing two parameters. The special choice of these parameters makes the system integrable in the Liouville sense. Its equations of motions were interpreted by \textit{A. P. Fordy} as stationary flows of some soliton equations of fifth order [Physica D 52, No. 2/3, 204--210 (1991; Zbl 0753.35102)]. The author constructs and studies a hierarchy of multidimensional generalizations of Hénon-Heiles systems obtained as constrained flows of the Korteweg-de Vries hierarchy. The last method, formulated by \textit{M. Antonowicz} and \textit{S. Rauch-Wojciechowski} [Phys. Lett. A 147, No. 8-9, 455--462 (1990)], generates finite-dimensional integrable systems from a given infinite-dimensional integrable system (constrained (or restricted) flows are essentially a new parameterization of stationary flows). The author derives (in rather technical way) the Lax representation, classical Poisson structure and \(r\)-matrix for the obtained hierarchy. Finally, he separates variables in the Hamilton-Jacobi equation (defining new variables as zeros of some polynom associated with the Lax representation) and constructs a Jacobi inversion problem for the hierarchy.
reviewed by: Jan L. Cieśliński
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 35Q53
zbMATH DE Number: 1530096
zbMATH Keywords: higher-order constrained flow
zbMATH Keywords: multidimensional Hénon-Heiles systems
zbMATH Keywords: Lax representation
zbMATH Keywords: Jacobi inversion problem
MaRDI profile type: Publication
full work available at URL: s101140000045
OpenAlex ID: W2086641095
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DOI: 10.1007/S101140000045
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published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 1530096