A pasting lemma and some applications for conservative systems

We prove that in a compact manifold of dimension n≥2, C1+α volume-preserving diffeomorphisms that are robustly transitive in the C1-topology have a dominated splitting. Also we prove that for three-dimensional compact manifolds, an isolated robustly transitive invariant set for a divergence-free vec...

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Bibliographic Details
Published in:Ergodic theory and dynamical systems 2007-10, Vol.27 (5), p.1399-1417
Main Authors: ARBIETO, ALEXANDER, MATHEUS, CARLOS
Format: Article
Language:English
Subjects:
Business growth
Dynamical systems
Mathematical analysis
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Summary:We prove that in a compact manifold of dimension n≥2, C1+α volume-preserving diffeomorphisms that are robustly transitive in the C1-topology have a dominated splitting. Also we prove that for three-dimensional compact manifolds, an isolated robustly transitive invariant set for a divergence-free vector field cannot have a singularity. In particular, we prove that robustly transitive divergence-free vector fields in three-dimensional manifolds are Anosov. For this, we prove a ‘pasting’ lemma, which allows us to make perturbations in conservative systems.
ISSN:0143-3857
1469-4417
DOI:10.1017/S014338570700017X