A generic incompressible flow is topological mixing
type: Item
instance of: scholarly article
title: A generic incompressible flow is topological mixing
zbMATH Open document ID: 1157.37014
author: Mário Bessa
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2008-11-28T00:00:00Z
review text: Let \(M\) be an \(n\)-dimensional compact, connected, boundaryless \(C^{\infty}\) Riemannian manifold and \(\mu\) be the measure induced by a volume-form defined on \(M\), \(\mathfrak{X}_{\mu}^r(M)\) be for any \(r\geq 1\) the class of \(C^r\) divergence-free vector fields on \(M\). It is proved that in \(\mathfrak{X}_{\mu}^r(M)\) there exists a residual subset, such that any vector field in it has the following property: For any two nonempty open subsets \(U\) and \(V\) on \(M\) there exists \(\tau \in \mathbb{R}\) such that \(X^t(U)\bigcap V\neq \emptyset\) for any \(t\geq \tau.\) Here \(X^t\) is an associated flow with any \(C^1\) vector field \(X\), which is an \(1\)-parameter group of a \(C^1\) volume-preserving diffeomorphisms and called as incompressible flow.
Mathematics Subject Classification ID: 37D40
Mathematics Subject Classification ID: 37D10
zbMATH DE Number: 5374916
zbMATH Keywords: compact, connected Riemannian manifold
zbMATH Keywords: divergence-free vector fields
zbMATH Keywords: residual subset existence with special property
reviewed by: Boris V. Loginov
MaRDI profile type: Publication
full work available at URL: j.crma.2008.07.012
OpenAlex ID: W1972475990
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DOI: 10.1016/J.CRMA.2008.07.012
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description: scientific article; zbMATH DE number 5374916