Controllability of families of measure preserving vector fields
type: Item
instance of: scholarly article
title: Controllability of families of measure preserving vector fields
zbMATH Open document ID: 0626.49017
DOI: 10.1016/0167-6911(87)90087-9
author: Luiz A. B. San Martin
published in: Systems \& Control Letters
publication date: 1987-01-01T00:00:00Z
review text: The author considers a family \(\Sigma\) of vector fields on a differentiable manifold M endowed with a probability measure m. The vector fields are assumed to preserve the measure m. The author proves that if \(\Sigma\) is transitive (i.e., if each point of M is reachable from each other along onward or backward trajectories of \(\Sigma)\) then for every initial point in an open dense and connected subset of M, the closure of the reachable set is equal to M. The paper also contains some examples.
reviewed by: Andrea Bacciotti
Mathematics Subject Classification ID: 93B03
Mathematics Subject Classification ID: 57R27
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 28D99
zbMATH DE Number: 4017737
zbMATH Keywords: accessibility
zbMATH Keywords: vector fields on a differentiable manifold
zbMATH Keywords: probability measure
zbMATH Keywords: closure of the reachable set
MaRDI profile type: Publication
full work available at URL: 0167-6911(87)90087-9
OpenAlex ID: W2156519538
cites work: Q3234755
cites work: Controllability of Nonlinear Systems on Compact Manifolds
cites work: Q3783191
cites work: Orbits of Families of Vector Fields and Integrability of Distributions
description: scientific article; zbMATH DE number 4017737