78 citations · 288 across the 45 of their papers we have counts for
56 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…
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…
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 le…
Partially hyperbolic diffeormorphisms, ergodicity, and transverse foliations in dimension 3
S. R. Fenley, R. Potrie
We give a complete topological classification of (chain-)transitive partially hyperbolic diffeomorphisms in 3-manifolds in terms of Anosov flows, completing a program proposed by P…
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…
Horizontality of partially hyperbolic foliations
Andy Hammerlindl, Rafael Potrie
We show exactly which Seifert manifolds support partially hyperbolic dynamical systems. In particular, a circle bundle over a higher-genus surface supports a partially hyperbolic s…