38 citations · 309 across the 47 of their papers we have counts for
6 papers · 1 filter
Periodic measures and partially hyperbolic homoclinic classes
Christian Bonatti, Jinhua Zhang
In this paper, we give a precise meaning to the following fact, and we prove it: -open and densely, all the non-hyperbolic ergodic measures generated by a robust cycle are app…
A criterion for zero averages and full support of ergodic measures
Christian Bonatti, Lorenzo J. Diaz, Jairo Bochi
Consider a homeomorphism defined on a compact metric space and a continuous map . We provide an abstract criterion, called \emph{control at any sc…
What is ... a blender?
Christian Bonatti, Sylvain Crovisier, Lorenzo Diaz +1
What is a blender? In six illustrated pages we define the construction of a blender and the role it plays in the study of smooth dynamical systems.
On the existence of non-hyperbolic ergodic measures as the limit of periodic measures
Christian Bonatti, Jinhua Zhang
[GIKN] and [BBD1] propose two very different ways for building non hyperbolic measures, [GIKN] building such a measure as the limit of periodic measures and [BBD1] as the -limit…
Many intermingled basins in dimension 3
Christian Bonatti, Rafael Potrie
We construct a diffeomorphism of admitting any finite or countable number of physical measures with intermingled basins. The examples are partially hyperbolic with s…
Transverse foliations on the torus $\T^2$ and partially hyperbolic diffeomorphisms on 3-manifolds
Christian Bonatti, Jinhua Zhang
In this paper, we prove that given two foliations and on which are transverse, there exists a non-null homotopic loop $\{Φ_t\}_{t\i…