On the weak Kowalevski-Painlevé property for hyperelliptically separable systems
type: Item
instance of: scholarly article
title: On the weak Kowalevski-Painlevé property for hyperelliptically separable systems
zbMATH Open document ID: 0984.37068
DOI: 10.1023/A:1006425609939
author: S. Abenda
author: Yuri N. Fedorov
published in: Acta Applicandae Mathematicae
publication date: 2002-05-01T00:00:00Z
review text: The authors consider a class of finite-dimensional integral systems having the weak Kowalevski-Painlevé property, which generalizes the notion of algebraic complete integrability. The authors allow that their real invariant \(N\)-dimensional Liouville tori are extended to \(N\)-dimensional complex analytic nonlinear subvarieties of Abelian tori of dimension \(g\geq n\), so-called strata. Here, the nonlinearity means that such subvarieties are not complex Abelian groups. Moreover, the authors require that on universal coverings of the Abelian tori there exists coordinates \(\varphi_1,\dots, \varphi_g\) such that under the Hamiltonian flow, \(\varphi_1,\dots, \varphi_N\) change linearly in time \(t\), whereas the rest of the coordinates are analytic functions of the former. Some model examples are considered, such as the hierarchy of integrable generalizations of the Hénon-Heiles and the Neumann systems.
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 14H40
Mathematics Subject Classification ID: 37J40
Mathematics Subject Classification ID: 14H70
zbMATH DE Number: 1506490
zbMATH Keywords: Kowalevski-Painlevé property
zbMATH Keywords: complete integrability
zbMATH Keywords: Liouville tori
zbMATH Keywords: Hamiltonian flow
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: a:1006425609939
OpenAlex ID: W2380337308
description: scientific article; zbMATH DE number 1506490