11 citations · 45 across the 13 of their papers we have counts for
13 papers
On physical measures of multi-singular hyperbolic vector fields
Sylvain Crovisier, Xiaodong Wang, Dawei Yang +1
Bonatti and da Luz have introduced the class of \emph{multi-singular hyperbolic} vector fields to characterize systems whose periodic orbits and singularities do not bifurcate unde…
Disintegrations of non-hyperbolic ergodic measures along the center foliation of DA maps
Ali Tahzibi, Jinhua Zhang
We show that each non-hyperbolic ergodic measure of a partially hyperbolic diffeomorphism on which is homotopic to Anosov admits a full measure subset which intersec…
Centralizers of derived-from-Anosov systems on : rigidity versus triviality
Shaobo Gan, Yi Shi, Disheng Xu +1
In this paper, we study the centralizer of a partially hyperbolic diffeomorphism on which is homotopic to an Anosov automorphism, and we show that either its central…
Ergodic optimization for some dynamical systems beyond uniform hyperbolicity
Dawei Yang, Jinhua Zhang
In this paper, we show that for several interesting systems beyond uniform hyperbolicity, any generic continuous function has a unique maximizing measure with zero entropy. In some…
On the notions of singular domination and (multi-)singular hyperbolicity
Sylvain Crovisier, Adriana da Luz, Dawei Yang +1
The properties of uniform hyperbolicity and dominated splitting have been introduced to study the stability of the dynamics of diffeomorphisms. One meets difficulties when one trie…
Transitive partially hyperbolic diffeomorphisms with one-dimensional neutral center
Christian Bonatti, Jinhua Zhang
In this paper, we study transitive partially hyperbolic diffeomorphisms with one-dimensional topologically neutral center, meaning that the length of the iterate of small center se…
Empirical measures of partially hyperbolic attractors
Sylvain Crovisier, Dawei Yang, Jinhua Zhang
In this paper, we study the limit measures of the empirical measures of Lebesgue almost every point in the basin of a partially hyperbolic attractor. They are strongly related to a…
Non-hyperbolic ergodic measures and horseshoes in partially hyperbolic homoclinic classes
Dawei Yang, Jinhua Zhang
We study a rich family of robustly non-hyperbolic transitive diffeomorphisms and we show that each ergodic measure is approached by hyperbolic sets in weak-topology and in entro…
Partially hyperbolic diffeomorphisms with one-dimensional neutral center on 3-manifolds
Jinhua Zhang
We prove that for any partially hyperbolic diffeomorphism with one dimensional neutral center on a 3-manifold, the center stable and center unstable foliations are complete; moreov…
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…
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…
Ergodic measures with multi-zero Lyapunov exponents inside homoclinic classes
Xiaodong Wang, Jinhua Zhang
We prove that for generic diffeomorphisms, if a homoclinic class contains two hyperbolic periodic orbits of indices and respectively and has no domina…
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…