Partial hyperbolicity far from homoclinic bifurcations (2008)
We prove that any diffeomorphism of a compact manifold can be C^1-approximated by a diffeomorphism which exhibits a homoclinic bifurcation (a homoclinic tangency or a heterodimensional cycle) or by a...
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...
Realisation of measured dynamics as uniquely ergodic minimal homeomorphisms on manifolds (2008)
Béguin, François, Crovisier, Sylvain, Roux, Frédéric Le
We prove that the family of measured dynamical systems which can be realised as uniquely ergodic minimal homeomorphisms on a given manifold (of dimension at least two) is stable under measured...
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.
Realisation of measured dynamics as uniquely ergodic minimal homeomorphisms on manifolds (2008)
Béguin, François, Crovisier, Sylvain, Le Roux, Frédéric
We prove that the family of measured dynamical systems which can be realised as uniquely ergodic minimal homeomorphisms on a given manifold (of dimension at least two) is stable under measured...
Realisation of measured dynamics as uniquely ergodic minimal homeomorphisms on manifolds (2008)
Béguin, François, Crovisier, Sylvain, Le Roux, Frédéric
We prove that the family of measured dynamical systems which can be realised as uniquely ergodic minimal homeomorphisms on a given manifold (of dimension at least two) is stable under measured...
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...
Partial hyperbolicity far from homoclinic bifurcations (2008)
We prove that any diffeomorphism of a compact manifold can be C^1-approximated by a diffeomorphism which exhibits a homoclinic bifurcation (a homoclinic tangency or a heterodimensional cycle) or by a...
Partial hyperbolicity far from homoclinic bifurcations (2008)
We prove that any diffeomorphism of a compact manifold can be C^1-approximated by a diffeomorphism which exhibits a homoclinic bifurcation (a homoclinic tangency or a heterodimensional cycle) or by a...
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...
Denjoy constructions for fibred homeomorphisms of the torus (2007)
Béguin, François, Crovisier, Sylvain, Jaeger, Tobias, Roux, Frédéric Le
We construct different types of quasiperiodically forced circle homeomorphisms with transitive but non-minimal dynamics. Concerning the recent Poincar\'e-like classification for this class of maps of...
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...
Denjoy constructions for fibred homeomorphisms of the torus (2007)
Béguin, François, Crovisier, Sylvain, Jaeger, Tobias, Le Roux, Frédéric
We construct different types of quasiperiodically forced circle homeomorphisms with transitive but non-minimal dynamics. Concerning the recent Poincar\'e-like classification for this class of maps of...
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...
Denjoy constructions for fibred homeomorphisms of the torus (2007)
Béguin, François, Crovisier, Sylvain, Jaeger, Tobias, Le Roux, Frédéric
We construct different types of quasiperiodically forced circle homeomorphisms with transitive but non-minimal dynamics. Concerning the recent Poincar\'e-like classification for this class of maps of...
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...
Béguin, François, Crovisier, Sylvain, Le Roux, Frédéric
Mary Rees has constructed a minimal homeomorphism of the 2-torus with positive topological entropy. This homeomorphism f is obtained by enriching the dynamics of an irrational rotation R. We improve...
Béguin, François, Crovisier, Sylvain, Le Roux, Frédéric
Mary Rees has constructed a minimal homeomorphism of the 2-torus with positive topological entropy. This homeomorphism f is obtained by enriching the dynamics of an irrational rotation R. We improve...
We prove a conjecture of J. Palis: any diffeomorphism of a compact manifold can be C1-approximated by a Morse-Smale diffeomorphism or by a diffeomorphism having a transverse homoclinic intersection....
Béguin, François, Crovisier, Sylvain, Roux, Frédéric Le
Mary Rees has constructed a minimal homeomorphism of the 2-torus with positive topological entropy. This homeomorphism f is obtained by enriching the dynamics of an irrational rotation R. We improve...
We prove a conjecture of J. Palis: any diffeomorphism of a compact manifold can be C1-approximated by a Morse-Smale diffeomorphism or by a diffeomorphism having a transverse homoclinic intersection....
We prove a conjecture of J. Palis: any diffeomorphism of a compact manifold can be C1-approximated by a Morse-Smale diffeomorphism or by a diffeomorphism having a transverse homoclinic intersection....
We prove a conjecture of J. Palis: any diffeomorphism of a compact manifold can be C1-approximated by a Morse-Smale diffeomorphism or by a diffeomorphism having a transverse homoclinic intersection....
Béguin, François, Crovisier, Sylvain, Le Roux, Frédéric
Mary Rees has constructed a minimal homeomorphism of the 2-torus with positive topological entropy. This homeomorphism f is obtained by enriching the dynamics of an irrational rotation R. We improve...
Béguin, François, Crovisier, Sylvain, Le Roux, Frédéric
Mary Rees has constructed a minimal homeomorphism of the 2-torus with positive topological entropy. This homeomorphism f is obtained by enriching the dynamics of an irrational rotation R. We improve...
Pseudo-rotations of the closed annulus : variation on a theorem of J. Kwapisz (2003)
Crovisier, Sylvain, Beguin, Francois, Roux, Frederic Le, Patou, Alice
Consider a homeomorphism h of the closed annulus S^1*[0,1], isotopic to the identity, such that the rotation set of h is reduced to a single irrational number alpha (we say that h is an irrational...
Pseudo-rotations of the closed annulus : variation on a theorem of J. Kwapisz (2003)
Crovisier, Sylvain, Beguin, Francois, Le Roux, Frederic, Patou, Alice
Consider a homeomorphism h of the closed annulusS^1*[0,1], isotopic to the identity, such that therotation set of h is reduced to a single irrationalnumber alpha (we say that h is an...
Pseudo-rotations of the closed annulus : variation on a theorem of J. Kwapisz (2003)
Crovisier, Sylvain, Beguin, Francois, Le Roux, Frederic, Patou, Alice
Consider a homeomorphism h of the closed annulusS^1*[0,1], isotopic to the identity, such that therotation set of h is reduced to a single irrationalnumber alpha (we say that h is an...
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...
Pseudo-rotations of the closed annulus : variation on a theorem of J. Kwapisz (2003)
Crovisier, Sylvain, Beguin, Francois, Le Roux, Frederic, Patou, Alice
Consider a homeomorphism h of the closed annulusS^1*[0,1], isotopic to the identity, such that therotation set of h is reduced to a single irrationalnumber alpha (we say that h is an...
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...
Pseudo-rotations of the closed annulus : variation on a theorem of J. Kwapisz (2003)
Crovisier, Sylvain, Beguin, Francois, Le Roux, Frederic, Patou, Alice
Consider a homeomorphism h of the closed annulusS^1*[0,1], isotopic to the identity, such that therotation set of h is reduced to a single irrationalnumber alpha (we say that h is an...
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...
Nombre de rotation et dynamique faiblement hyperbolique. (2002)
Cette thèse s'appuie sur deux branches des systèmes dynamiques : la théorie du nombre de rotation des endomorphismes du cercle de degré un et des applications de l'anneau déviant la verticale,...
Nombre de rotation et dynamique faiblement hyperbolique. (2001)
Cette thèse s'appuie sur deux branches des systèmes dynamiques : la théorie du nombre de rotation des endomorphismes du cercle de degré un et des applications de l'anneau déviant la verticale,...
Nombre de rotation et dynamique faiblement hyperbolique. (2001)
Cette thèse s'appuie sur deux branches des systèmes dynamiques : la théorie du nombre de rotation des endomorphismes du cercle de degré un et des applications de l'anneau déviant la verticale,...
Nombre de rotation et dynamique faiblement hyperbolique. (2001)
Cette thèse s'appuie sur deux branches des systèmes dynamiques : la théorie du nombre de rotation des endomorphismes du cercle de degré un et des applications de l'anneau déviant la verticale,...
Nombre de rotation et dynamique faiblement hyperbolique. (2001)
Cette thèse s'appuie sur deux branches des systèmes dynamiques : la théorie du nombre de rotation des endomorphismes du cercle de degré un et des applications de l'anneau déviant la verticale,...
Nombre de rotation et dynamique faiblement hyperbolique. (2001)
Cette thèse s'appuie sur deux branches des systèmes dynamiques : la théorie du nombre de rotation des endomorphismes du cercle de degré un et des applications de l'anneau déviant la verticale,...
Nombre de rotation et dynamique faiblement hyperbolique. (2001)
Cette thèse s'appuie sur deux branches des systèmes dynamiques : la théorie du nombre de rotation des endomorphismes du cercle de degré un et des applications de l'anneau déviant la verticale,...