Trajectories of a dynamical system determined by a one-parameter group of conformal mappings of \(R^ 3\)
type: Item
instance of: scholarly article
title: Trajectories of a dynamical system determined by a one-parameter group of conformal mappings of \(R^ 3\)
zbMATH Open document ID: 0544.58022
DOI: 10.1007/BF00968795
author: L. N. Pestov
author: Vladimir Golubyatnikov
published in: Siberian Mathematical Journal
publication date: 1983-01-01T00:00:00Z
review text: In the three-dimensional space we consider trajectories of a dynamical system generated by a one-parameter group of conformal maps in \(R^ 3\). The systems of this type arise if there exists the first integral linear with respect to the velocity vector in the system of equations of geodesic lines in Riemannian spaces with a conformally flat metric. If the dynamical system has a singular point, it can be linearized by a conformal map. If there are no singular points, we find a family of integral manifolds (tori) around which the trajectories are wound.
Mathematics Subject Classification ID: 37-XX
zbMATH DE Number: 3866247
zbMATH Keywords: trajectories
zbMATH Keywords: dynamical system
zbMATH Keywords: conformal map
MaRDI profile type: Publication
cites work: Sur les courbes definies par les équations différentielles à la surface du tore
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description: scientific article; zbMATH DE number 3866247