Add to ORKGWe study the dynamics of homoclinic classes on three dimensionalmanifolds under the robust absence of dominated splittings. We prove that, C1-generically, if such a homoclinic class contains a volume-expanding periodic point, then it contains a hyperbolic periodic point whose index(dimension of the unstable manifold) is equal to two. We also furnish anexample which shows that a similar result is not always true in higherdimensions.University of Tokyo (東京大学
International audienceWe prove that, for $C^1$-generic diffeomorphisms, if a homoclinic class is not...
We show that, for Cl-generic diffeornorphisms, every chain recurrent class C that has a partially hy...
We study a diffeomorphism of a multidimensional space into itself with a hyperbolic fixed point at ...
We study the dynamics of homoclinic classes on three dimensionalmanifolds under the robust absence o...
Let f: M → M be a diffeomorphism defined in a d-dimensional com-pact boundary-less manifold M. We pr...
International audienceWe prove that there is a residual subset I of Diff such that any homoclinic cl...
Abstract. Let f be a diffeomorphism of a compact C ∞ manifold, and let p be a hyperbolic periodic po...
We consider diffeomorphism of three-dimensional space with a hyperbolic fixed point at the origin an...
We consider the vector fields C1 on a compact Riemannian manifold, boundaryless of finite dimension n,...
Abstract. Let Mn be a compact n-dimensional manifold and! be a symplectic or volume form on Mn. Let ...
In this paper, we revisit uniformly hyperbolic basic sets and the dom- ination of Oseledets splittin...
Let f be a diffeomorphism of a closed n-dimensional C-infinity manifold, and p be a hyperbolic saddl...
It is known that all non-hyperbolic robustly transitive sets Λφ have a dominated splitting and, gene...
The dynamics of a diffeomorphism of a compact manifold concentrates essentially on the chain recurre...
We consider a diffeomorphism of a plane into itself with a fixed hyperbolic point at the origin and a ...
International audienceWe prove that, for $C^1$-generic diffeomorphisms, if a homoclinic class is not...
We show that, for Cl-generic diffeornorphisms, every chain recurrent class C that has a partially hy...
We study a diffeomorphism of a multidimensional space into itself with a hyperbolic fixed point at ...
We study the dynamics of homoclinic classes on three dimensionalmanifolds under the robust absence o...
Let f: M → M be a diffeomorphism defined in a d-dimensional com-pact boundary-less manifold M. We pr...
International audienceWe prove that there is a residual subset I of Diff such that any homoclinic cl...
Abstract. Let f be a diffeomorphism of a compact C ∞ manifold, and let p be a hyperbolic periodic po...
We consider diffeomorphism of three-dimensional space with a hyperbolic fixed point at the origin an...
We consider the vector fields C1 on a compact Riemannian manifold, boundaryless of finite dimension n,...
Abstract. Let Mn be a compact n-dimensional manifold and! be a symplectic or volume form on Mn. Let ...
In this paper, we revisit uniformly hyperbolic basic sets and the dom- ination of Oseledets splittin...
Let f be a diffeomorphism of a closed n-dimensional C-infinity manifold, and p be a hyperbolic saddl...
It is known that all non-hyperbolic robustly transitive sets Λφ have a dominated splitting and, gene...
The dynamics of a diffeomorphism of a compact manifold concentrates essentially on the chain recurre...
We consider a diffeomorphism of a plane into itself with a fixed hyperbolic point at the origin and a ...
International audienceWe prove that, for $C^1$-generic diffeomorphisms, if a homoclinic class is not...
We show that, for Cl-generic diffeornorphisms, every chain recurrent class C that has a partially hy...
We study a diffeomorphism of a multidimensional space into itself with a hyperbolic fixed point at ...
