36 citations · 100 across the 13 of their papers we have counts for
11 papers · 1 filter
Construction of Anosov flows on fibered hyperbolic 3-manifolds
François Béguin, Christian Bonatti, Biao Ma +1
We prove that fibered hyperbolic -manifolds carrying transitive Anosov flows are abundant. More precisely, for every , there is a finite index subgroup~ of $ \mathrm…
Heterodimensional cycles of hyperbolic ergodic measures
Christian Bonatti, Lorenzo J. Diaz, Katrin Gelfert
We introduce the concept of a heterodimensional cycle of hyperbolic ergodic measures and a special type of them that we call rich. Within a partially hyperbolic context, we prove t…
Action on the circle at infinity of foliations of
Christian Bonatti
This paper provides a canonical compactification of the plane by adding a circle at infinity associated to a countable family of singular foliations or laminations…
Oriented Birkhoff sections of Anosov flows
Masayuki Asaoka, Christian Bonatti, Théo Marty
This paper gives 3 different proofs (independently obtained by the 3 authors) of the following fact: given an Anosov flow on an oriented 3 manifold, the existence of a positive Bir…
Aperiodic chain recurrence classes of -generic diffeomorphisms
Christian Bonatti, Katsutoshi Shinohara
We consider the space of -diffeomorphims equipped with the -topology on a three dimensional closed manifold. It is known that there are open sets in which -generic d…
A mechanism for ejecting a horseshoe from a partially hyperbolic chain recurrence class
Christian Bonatti, Katsutoshi Shinohara
We give a -perturbation technique for ejecting an a priori given finite set of periodic points preserving a given finite set of homo/hetero-clinic intersections from a chain r…