22 citations · 58 across the 10 of their papers we have counts for
10 papers
Shub's example revisited
Chao Liang, Radu Saghin, Fan Yang +1
For a class of robustly transitive diffeomorphisms on introduced by Shub in [24], satisfying an additional bunching condition, we show that there exits a open a…
-openness of non-uniform hyperbolic diffeomorphisms with bounded norm
Chao Liang, Karina Marin, Jiagang Yang
We study the -topological properties of the subset of non-uniform hyperbolic diffeomorphisms in a certain class of partially hyperbolic symplectic systems which have bou…
Lyapunov exponents of partially hyperbolic volume-preserving maps with 2-dimensional center bundle
Chao Liang, Karina Marin, Jiagang Yang
We consider the set of partially hyperbolic symplectic diffeomorphisms which are accessible, have 2-dimensional center bundle and satisfy some pinching and bunching conditions. In…
The density of nonuniform hyperbolicity in conservative diffeomorphisms
Chao Liang, Yun Yang
Let $\Diff^{ r}_m(M)$ be the set of volume-preserving diffeomorphisms on a compact Riemannian manifold (). In this paper, we prove that the diffeomorphis…
On density of positive Lyapunov exponents for symplectic diffeomorphisms
Chao Liang
Let be a 2dimensional compact connected Riemannian manifold and be a symplectic form on . In this paper, we prove that a symplectic diffeomorphism, with all Lyapunov…
Approximation of Oseledets Splittings
Chao Liang, Gang Liao, Wenxiang Sun
We prove that the Oseledets splittings of an ergodic hyperbolic measure of a diffeomorphism can be approximated by that of atomic measures on hyperbolic periodic orbits.…
Variational equalities of entropy in nonuniformly hyperbolic systems
Chao Liang, Gang Liao, Wenxiang Sun +1
In this paper we prove that for an ergodic hyperbolic measure of a diffeomorphism on a Riemannian manifold , there is an -full measured set su…
Ergodic Properties of Invariant Measures for C^{1+α} nonuniformly hyperbolic systems
Chao Liang, Wenxiang Sun, Xueting Tian
For an ergodic hyperbolic measure of a diffeomorphism, there is an full-measured set such that every nonempty, compact and connected subset of $\mat…
Some results on perturbations to Lyapunov exponents
Chao Liang, Wenxiang Sun, Jiagang Yang
In this paper, we study two properties of the Lyapunov exponents under small perturbations: one is when we can remove zero Lyapunov exponents and the other is when we can distingui…
Circle bundles over 4-manifolds
Haibao Duan, Chao Liang
Every 1-connected topological 4-manifold M admits a -covering by $#_{r-1}S^{2}\times S^{3}$, where rank$H^{2}(M;\QTR{Bbb}{Z})$.