Global analytic integrability of the Rabinovich system
type: Item
instance of: scholarly article
title: Global analytic integrability of the Rabinovich system
zbMATH Open document ID: 1184.34024
author: Claudia Valls
author: Jaume Llibre
published in: Journal of Geometry and Physics
publication date: 2008-12-10T00:00:00Z
review text: The authors consider the Rabinovich differential system \[ \dot{x}=hy-v_1x+yz,\quad \dot{y}=hx-v_2y-xz,\quad \dot{z}=-v_3z+xy \tag{1} \] with \(h, v_1, v_2, v_3\) being real parameters. Sufficient conditions for the existence and nonexistence of a global analytic first integral of (1) are given.
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 34A05
zbMATH DE Number: 5380139
zbMATH Keywords: analytic first integral
zbMATH Keywords: Rabinovich system
reviewed by: Sergei A. Mazanik
MaRDI profile type: Publication
full work available at URL: j.geomphys.2008.08.009
OpenAlex ID: W2054424743
cites work: On the complete and partial integrability of non-Hamiltonian systems
cites work: Integrals of motion for three-dimensional non-Hamiltonian dynamical systems
cites work: Formal and analytic integrability of the Lorenz system
cites work: Formal and analytic first integrals of the Einstein–Yang–Mills equations
cites work: Formal and analytical integrability of the Bianchi IX system
cites work: Q3335060
cites work: Invariant algebraic surfaces of the Rabinovich system
cites work: Integrals of motion of the Rabinovich system
DOI: 10.1016/J.GEOMPHYS.2008.08.009
description: scientific article; zbMATH DE number 5380139