Dynamical Systems
A generic incompressible flow is topological mixing
Comptes Rendus. Mathématique, Volume 346 (2008) no. 21-22, pp. 1169-1174.

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 τR such that Xt(U)V for any tτ.

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 XR est topologiquement mélangeant.

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Accepted:
Published online:
DOI: 10.1016/j.crma.2008.07.012
Bessa, Mário 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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Bessa, Mário. 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. http://www.numdam.org/articles/10.1016/j.crma.2008.07.012/

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