Integral curves of derivations on locally semi-algebraic differential spaces
type: Item
instance of: scholarly article
title: Integral curves of derivations on locally semi-algebraic differential spaces
zbMATH Open document ID: 1086.53100
published in: Discrete and Continuous Dynamical Systems
publication date: 2004-02-23T00:00:00Z
review text: The reduction of symmetries of Hamiltonian systems in terms of differential spaces is studied. The definition of differential spaces is given and their properties are presented. Then, the closed differential subspaces of Euclidean and Hausdorff differential spaces that are locally diffeomorphic to closed subsets of Euclidean space are considered. The derivations on differential space structures are introduced and the associated integral curves are defined. A class of differential spaces which contains orbit spaces of proper actions of Lie groups on smooth manifolds is identified. The existence and uniqueness theorem for integral curves of derivations of smooth functions is proven for this class. A necessary and sufficient condition for a derivation to generate a local one-parameter group of local diffeomorphisms is also given. It is concluded that the results presented in this paper hold for all closed differential subspaces of Euclidean space and all differential spaces which are locally diffeomorphic to closed subsets of Euclidean space.
Mathematics Subject Classification ID: 53D20
Mathematics Subject Classification ID: 58A40
Mathematics Subject Classification ID: 37J15
zbMATH DE Number: 2046258
zbMATH Keywords: differential space
zbMATH Keywords: orbit space
zbMATH Keywords: derivation
zbMATH Keywords: integral curve
zbMATH Keywords: one parameter group
author: J. Śniatycki
reviewed by: Gheorghe Zet
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2046258