Robust transitivity of singular hyperbolic attractors Article - 2020

Sylvain Crovisier, Dawei Yang

Sylvain Crovisier, Dawei Yang, « Robust transitivity of singular hyperbolic attractors  », Mathematische Zeitschrift, à paraître. ISSN 0025-5874


Singular hyperbolicity is a weakened form of hyperbolicity that has been introduced for vector fields in order to allow non-isolated singularities inside the non-wandering set. A typical example of a singular hyperbolic set is the Lorenz attractor. However, in contrast to uniform hyperbolicity, singular hyperbolicity does not immediately imply robust topological properties, such as the transitivity. In this paper, we prove that open and densely inside the space of $C^1$ vector fields of a compact manifold, any singular hyperbolic attractors is robustly transitive.

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