On the existence of attractors (2009)
Bonatti, Christian, Li, Ming, Yang, Dawei
On every compact 3-manifold, we build a non-empty open set $\cU$ of $\Diff^1(M)$ such that, for every $r\geq 1$, every $C^r$-generic diffeomorphism $f\in\cU\cap \Diff^r(M)$ has no topological...
Roots in the mapping class groups (2009)
Bonatti, Christian, Paris, Luis
The purpose of this paper is to study the roots in the mapping class groups. Let Σ be a compact oriented surface, possibly with boundary, let 𝒫 be a finite set of punctures in the interior of...
Nonuniform hyperbolicity for C^1-generic diffeomorphisms (2008)
Abdenur, Flavio, Bonatti, Christian, Crovisier, Sylvain
We study the ergodic theory of non-conservative C^1-generic diffeomorphisms. First, we show that homoclinic classes of arbitrary diffeomorphisms exhibit ergodic measures whose supports coincide with...
The C1 generic diffeomorphism has trivial centralizer (2008)
Bonatti, Christian, Crovisier, Sylvain, Wilkinson, Amie
Answering a question of Smale, we prove that the space of C1 diffeomorphisms of a compact manifold contains a residual subset of diffeomorphisms whose centralizers are trivial.
The C1 generic diffeomorphism has trivial centralizer (2008)
Bonatti, Christian, Crovisier, Sylvain, Wilkinson, Amie
Answering a question of Smale, we prove that the space of C1 diffeomorphisms of a compact manifold contains a residual subset of diffeomorphisms whose centralizers are trivial.
The C1 generic diffeomorphism has trivial centralizer (2008)
Bonatti, Christian, Crovisier, Sylvain, Wilkinson, Amie
Answering a question of Smale, we prove that the space of C1 diffeomorphisms of a compact manifold contains a residual subset of diffeomorphisms whose centralizers are trivial.
Nonuniform hyperbolicity for C^1-generic diffeomorphisms (2008)
Abdenur, Flavio, Bonatti, Christian, Crovisier, Sylvain
We study the ergodic theory of non-conservative C^1-generic diffeomorphisms. First, we show that homoclinic classes of arbitrary diffeomorphisms exhibit ergodic measures whose supports coincide with...
Nonuniform hyperbolicity for C^1-generic diffeomorphisms (2008)
Abdenur, Flavio, Bonatti, Christian, Crovisier, Sylvain
We study the ergodic theory of non-conservative C^1-generic diffeomorphisms. First, we show that homoclinic classes of arbitrary diffeomorphisms exhibit ergodic measures whose supports coincide with...
Existence de points fixes enlac\'es \`a une orbite p\'eriodique d'un hom\'eomorphisme du plan (2007)
Bonatti, Christian, Kolev, Boris
Let f be an orientation-preserving homeomorphism of the plane such that f-Id is contracting. Under these hypotheses, we establish the existence, for every periodic orbit, of a fixed point which has...
Ju Ne, Viviane Baladi, Christian Bonatti, Bernard Schmitt
. Consider a C 1+ffl diffeomorphism f having a uniformly hyperbolic compact invariant set \Omega\Gamma maximal invariant in some small neighbourhood of itself. The asymptotic exponential rate of...
Généricité d’exposants de Lyapunov non-nuls pour des produits déterministes de matrices (2007)
Christian Bonatti, Marcelo Viana
We propose a geometric sucient criterium \a la Furstenberg " for the existence of non-zero Lyapunov exponents for certain linear cocycles over hyperbolic transformations: non-existence of...
Généricité d’exposants de Lyapunov non-nuls pour des produits déterministes de matrices (2007)
Christian Bonatti, Xavier Gómez-mont, Marcelo Viana
We propose a geometric sufficient criterium “à la Furstenberg ” for the existence of non-zero Lyapunov exponents for certain linear cocycles over hyperbolic transformations: non-existence of...
C1-generic conservative diffeomorphisms have trivial centralizer (2007)
Bonatti, Christian, Crovisier, Sylvain, Wilkinson, Amie
We prove that the spaces of C1 symplectomorphisms and of C1 volume-preserving diffeomorphisms of connected manifolds both contain residual subsets of diffeomorphisms whose centralizers are trivial....
Local density of diffeomorphisms with large centralizers (2007)
Bonatti, Christian, Crovisier, Sylvain, Vago, Gioia, Wilkinson, Amie
Given any compact manifold M, we construct a non-empty open subset O of the space of C^1-diffeomorphisms of M and a dense subset D of O such that the centralizer of every diffeomorphism in D is...
The centralizer of a C1 generic diffeomorphism is trivial (2007)
Bonatti, Christian, Crovisier, Sylvain, Wilkinson, Amie
In this announcement, we describe the solution in the C1 topology to a question asked by S. Smale on the genericity of trivial centralizers: the set of diffeomorphisms of a compact connected manifold...
Centralizers of C^1-generic diffeomorphisms (2007)
Bonatti, Christian, Crovisier, Sylvain, Wilkinson, Amie
On the one hand, we prove that the spaces of C^1 symplectomorphisms and of C^1 volume-preserving diffeomorphisms both contain residual subsets of diffeomorphisms whose centralizers are trivial. On...
The centralizer of a C1 generic diffeomorphism is trivial (2007)
Bonatti, Christian, Crovisier, Sylvain, Wilkinson, Amie
In this announcement, we describe the solution in the C1 topology to a question asked by S. Smale on the genericity of trivial centralizers: the set of diffeomorphisms of a compact connected manifold...
Local density of diffeomorphisms with large centralizers (2007)
Bonatti, Christian, Crovisier, Sylvain, Vago, Gioia, Wilkinson, Amie
Given any compact manifold M, we construct a non-empty open subset O of the space of C^1-diffeomorphisms of M and a dense subset D of O such that the centralizer of every diffeomorphism in D is...
C1-generic conservative diffeomorphisms have trivial centralizer (2007)
Bonatti, Christian, Crovisier, Sylvain, Wilkinson, Amie
We prove that the spaces of C1 symplectomorphisms and of C1 volume-preserving diffeomorphisms of connected manifolds both contain residual subsets of diffeomorphisms whose centralizers are trivial....
C1-generic conservative diffeomorphisms have trivial centralizer (2007)
Bonatti, Christian, Crovisier, Sylvain, Wilkinson, Amie
We prove that the spaces of C1 symplectomorphisms and of C1 volume-preserving diffeomorphisms of connected manifolds both contain residual subsets of diffeomorphisms whose centralizers are trivial....
Local density of diffeomorphisms with large centralizers (2007)
Bonatti, Christian, Crovisier, Sylvain, Vago, Gioia, Wilkinson, Amie
Given any compact manifold M, we construct a non-empty open subset O of the space of C^1-diffeomorphisms of M and a dense subset D of O such that the centralizer of every diffeomorphism in D is...
Centralizers of C^1-generic diffeomorphisms (2006)
Bonatti, Christian, Crovisier, Sylvain, Wilkinson, Amie
On the one hand, we prove that the spaces of C^1 symplectomorphisms and of C^1 volume-preserving diffeomorphisms both contain residual subsets of diffeomorphisms whose centralizers are trivial. On...
Roots in the mapping class groups (2006)
Bonatti, Christian, Paris, Luis
The purpose of this paper is the study of the roots in the mapping class groups. Let $\Sigma$ be a compact oriented surface, possibly with boundary, let $\PP$ be a finite set of punctures in the...
Surface homeomorphisms with zero dimensional singular set (2004)
Kolev, Boris, Bonatti, Christian
We prove that if f is an orientation-preserving homeomorphism of a closed orientable surface M whose singular set is totally disconnected, then f is topologically conjugate to a conformal...
Recurrence and genericity (2003)
Bonatti, Christian, Crovisier, Sylvain
We prove a C^1-connecting lemma for pseudo-orbits of diffeomorphisms on compact manifolds. We explore some consequences for C^1-generic diffeomorphisms. For instance, C^1-generic conservative...
Recurrence and genericity (2003)
Bonatti, Christian, Crovisier, Sylvain
We prove a C^1-connecting lemma for pseudo-orbits of diffeomorphisms on compact manifolds. We explore some consequences for C^1-generic diffeomorphisms. For instance, C^1-generic conservative...
Recurrence and genericity (2003)
Bonatti, Christian, Crovisier, Sylvain
We prove a C^1-connecting lemma for pseudo-orbits of diffeomorphisms on compact manifolds. We explore some consequences for C^1-generic diffeomorphisms. For instance, C^1-generic conservative...
$C^1$-generic dynamics: tame and wild behaviour (2003)
This paper gives a survey of recent results on the maximal transitive sets of $C^1$-generic diffeomorphisms.
A H\"older continuous vector field tangent to many foliations (2003)
Bonatti, Christian, Franks, John
We construct an example of a H\"older continuous vector field on the plane which is tangent to all foliations in a continuous family of pairwise distinct $C^1$ foliations. Given any $1 \le r
Surface homeomorphisms with zero dimensional singular set (2003)
Bonatti, Christian, Kolev, Boris
We prove that if f is an orientation-preserving homeomorphism of a closed orientable surface M whose singular set is totally disconnected, then f is topologically conjugate to a conformal...
Recurrence and genericity (2003)
Bonatti, Christian, Crovisier, Sylvain
We prove a C^1-connecting lemma for pseudo-orbits of diffeomorphisms on compact manifolds. We explore some consequences for C^1-generic diffeomorphisms. For instance, C^1-generic conservative...
Recurrence and genericity (2003)
Bonatti, Christian, Crovisier, Sylvain
We prove a C^1-connecting lemma for pseudo-orbits of diffeomorphisms on compact manifolds. We explore some consequences for C^1-generic diffeomorphisms. For instance, C^1-generic conservative...
Transitive Partially Hyperbolic Diffeomorphisms on 3-Manifolds (2003)
Christian Bonatti, Amie Wilkinson
The known examples of transitive partially hyperbolic diffeomorphisms on 3-manifolds belong to 3 basic classes: perturbations of skew products over an Anosov map of T², perturbations of the...
Abundance of Stable Ergodicity (2003)
Christian Bonatti, Carlos Matheus, Marcelo Viana, Amie Wilkinson
We consider the set PH! (M) of volume preserving partially hyperbolic dieomorphisms on a compact manifold having 1-dimensional center bundle. We show that the volume measure is ergodic, and even...
Transitive partially hyperbolic diffeomorphisms on 3-manifolds (2002)
ICM2002 Satellite Conference: New Directions in Dynamical Systems Abstracts (August 2002 Kyoto)
Transitive partially hyperbolic diffeomorphisms on 3-manifolds (2002)
ICM2002 Satellite Conference: New Directions in Dynamical Systems Abstracts (August 2002 Kyoto)
Minimality of Strong Stable and Unstable Foliations for Partially Hyperbolic Diffeomorphisms (2001)
Christian Bonatti, Lorenzo J. Díaz, Raúl Ures
We give a topological criterion for the minimality of the strong unstable (or stable) foliation of robustly transitive partially hyperbolic dieomorphisms.
SRB measures for partially hyperbolic systems whose central direction is mostly expanding (2000)
José F. Alves, Christian Bonatti, Marcelo Viana
We construct Sinai-Ruelle-Bowen (SRB) measures supported on partially hyperbolic sets of diffeomorphisms -- the tangent bundle splits into two invariant subbundles, one of which is uniformly...
SRB measures for partially hyperbolic systems whose central direction is mostly expanding (2000)
José F. Alves, Christian Bonatti, Marcelo Viana
We construct Sinai-Ruelle-Bowen (SRB) measures supported on partially hyperbolic sets of diffeomorphisms - the tangent bundle splits into two invariant subbundles, one of which is uniformly...
SRB measures for partially hyperbolic systems whose central direction is mostly expanding (2000)
José F. Alves, Christian Bonatti, Marcelo Viana
We construct Sinai-Ruelle-Bowen (SRB) measures supported on partially hyperbolic sets of diffeomorphisms -- the tangent bundle splits into two invariant subbundles, one of which is uniformly...
SRB measures for partially hyperbolic systems whose central direction is mostly expanding (2000)
Jos'e Alves Christian, Christian Bonatti, Marcelo Viana
We construct Sinai-Ruelle-Bowen (SRB) measures supported on partially hyperbolic sets of diffeomorphisms -- the tangent bundle splits into two invariant subbundles, one of which is uniformly...
SRB measures for partially hyperbolic systems whose central direction is mostly expanding (2000)
Jose F. Alves, Christian Bonatti, Marcelo Viana
We construct Sinai-Ruelle-Bowen (SRB) measures supported on partially hyperbolic sets of di#eomorphisms -- the tangent bundle splits into two invariant subbundles, one of which is uniformly...
SRB measures for partially hyperbolic systems whose central direction is mostly contracting (1999)
Christian Bonatti And, Christian Bonatti, Marcelo Viana, Dominated E
We consider partially hyperbolic diffeomorphisms preserving a splitting of the tangent bundle into a strong-unstable subbundle E uu (uniformly expanding) and a subbundle E c , dominated by E uu . We...
SRB measures for partially hyperbolic systems whose central direction is mostly contracting (1999)
Christian Bonatti, Marcelo Viana, Dominated E
We consider partially hyperbolic diffeomorphisms preserving a splitting of the tangent bundle into a strong-unstable subbundle E uu (uniformly expanding) and a subbundle E c , dominated by E uu . We...
SRB measures for partially hyperbolic systems whose central direction is mostly expanding (1999)
José F. Alves, Christian Bonatti, Marcelo Viana
We construct Sinai-Ruelle-Bowen (SRB) measures supported on partially hyperbolic sets of diffeomorphisms -- the tangent bundle splits into two invariant subbundles, one of which is uniformly...
SRB measures for partially hyperbolic systems whose central direction is mostly contracting (1999)
Christian Bonatti, Marcelo Viana, Dominated E
We consider partially hyperbolic dieomorphisms preserving a splitting of the tangent bundle into a strong-unstable subbundle E (uniformly expanding) and a subbundle E , dominated by E .
Surface homeomorphisms with zero dimensional singular set (1998)
Kolev, Boris, Bonatti, Christian
We prove that if f is an orientation-preserving homeomorphism of a closed orientable surface M whose singular set is totally disconnected, then f is topologically conjugate to a conformal...
Surface homeomorphisms with zero dimensional singular set (1998)
Kolev, Boris, Bonatti, Christian
We prove that if f is an orientation-preserving homeomorphism of a closed orientable surface M whose singular set is totally disconnected, then f is topologically conjugate to a conformal...
Existence de points fixes enlacés à une orbite périodique d'un homéomorphisme du plan (1992)
Kolev, Boris, Bonatti, Christian
Let f be an orientation-preserving homeomorphism of the plane such that f-Id is contracting. Under these hypotheses, we establish the existence, for every periodic orbit, of a fixed point which has...
Existence de points fixes enlacés à une orbite périodique d'un homéomorphisme du plan (1992)
Bonatti, Christian, Kolev, Boris
Let f be an orientation-preserving homeomorphism of the plane such that f-Id is contracting. Under these hypotheses, we establish the existence, for every periodic orbit, of a fixed point which has...
Existence de points fixes enlacés à une orbite périodique d'un homéomorphisme du plan (1992)
Bonatti, Christian, Kolev, Boris
Let f be an orientation-preserving homeomorphism of the plane such that f-Id is contracting. Under these hypotheses, we establish the existence, for every periodic orbit, of a fixed point which has...