A generic incompressible flow is topological mixing

Mário Bessa

doi:10.1016/j.crma.2008.07.012

Dynamical Systems

A generic incompressible flow is topological mixing

Presented by: Étienne Ghys

Mário Bessa ¹

¹ESTGOH – IPC, Rua General Santos Costa, 3400-124, Oliveira do Hospital and CMUP, Rua do Campo Alegre, 687, 4169-007 Porto, Portugal

Comptes Rendus. Mathématique, Volume 346 (2008) no. 21-22, pp. 1169-1174

Abstract (Original language)
Résumé

In this Note we prove that there exists a residual subset of the set of divergence-free vector fields defined on a compact, connected Riemannian manifold M, such that any vector field in this residual satisfies the following property: Given any two nonempty open subsets U and V of M, there exists $τ \in R$ such that $X^{t} (U) \cap V \neq \emptyset$ for any $t ⩾ τ$ .

Dans cette Note nous montrons qu'il existe une partie résiduelle $R$ dans l'ensemble des champs vectoriels qui préservent l'élément de volume pour laquelle tout $X \in R$ est topologiquement mélangeant.

Received: 2008-04-16
Accepted: 2008-07-16
Published online: 2008-10-15

DOI: 10.1016/j.crma.2008.07.012

Author's affiliations:

Mário Bessa ¹

¹ ESTGOH – IPC, Rua General Santos Costa, 3400-124, Oliveira do Hospital and CMUP, Rua do Campo Alegre, 687, 4169-007 Porto, Portugal

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     title = {A generic incompressible flow is topological mixing},
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     pages = {1169--1174},
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     number = {21-22},
     doi = {10.1016/j.crma.2008.07.012},
     language = {en},
}

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Mário Bessa. A generic incompressible flow is topological mixing. Comptes Rendus. Mathématique, Volume 346 (2008) no. 21-22, pp. 1169-1174. doi: 10.1016/j.crma.2008.07.012

References
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