13 papers
Robust transitivity versus trapping regions for partially hyperbolic diffeomorphisms
Sylvain Crovisier, Rafael Potrie
We show that among partially hyperbolic diffeomorphisms with one dimensional center there is a -open and dense subset for which either there is a proper quasi-attractor or bot…
On transverse -covered minimal foliations
Thierry Barbot, Sergio R. Fenley, Rafael Potrie
We study minimal transverse foliations which are -covered. If in addition the dimension of the ambient manifold is , and the foliations are Anosov foliations we give necessar…
Exotic codimension one Anosov flows
Sergio Fenley, Kathryn Mann, Rafael Potrie
We construct Anosov flows in certain circle bundles over closed hyperbolic 3-manifolds, producing counterexamples to a conjecture of Verjovsky. Some of these 4-manifolds admit infi…
Transverse minimal foliations on unit tangent bundles and applications
Sergio R. Fenley, Rafael Potrie
We show that if and are two transverse minimal foliations on then either they intersect in an Anosov foliation or there exists a Reeb-sur…
Invariant sets for homeomorphisms of hyperbolic 3-manifolds
Elena Gomes, Santiago Martinchich, Rafael Potrie
We prove that under some assumptions on how points escape to infinity in the universal cover, homeomorphisms of hyperbolic 3-manifolds are forced to have several invariant sets (in…
Propagation of regularity along unstable manifolds
Thibault Lefeuvre, Rafael Potrie
Let be a flow on a smooth closed connected manifold that preserves and expands a foliation . We establish a theorem of propagation of regularity along the l…