9 citations · 29 across the 12 of their papers we have counts for
12 papers · 1 filter
Dimension theory of group actions by circle diffeomorphisms II: Minimal sets
Weikun He, Yuxiang Jiao, Disheng Xu +1
We establish a dimension theory for smooth group actions on the circle. For finitely generated groups of real-analytic circle diffeomorphisms preserving a Cantor minimal set, we in…
Transitive centralizers and fibered partially hyperbolic systems
Danijela Damjanovic, Amie Wilkinson, Disheng Xu
We prove several rigidity results about the centralizer of a smooth diffeomorphism, concentrating on two families of examples: diffeomorphisms with transitive centralizer, and pert…
The Zimmer Program for partially hyperbolic actions
Danijela Damjanovic, Ralf Spatzier, Kurt Vinhage +1
Zimmer's superrigidity theorems on higher rank Lie groups and their lattices launched a program of study aiming to classify actions of semisimple Lie groups and their lattices, kno…
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…
Pathology and asymmetry: centralizer rigidity for partially hyperbolic diffeomorphisms
Danijela Damjanovic, Amie Wilkinson, Disheng Xu
We discover a rigidity phenomenon within the volume-preserving partially hyperbolic diffeomorphisms with -dimensional center. In particular, for smooth, ergodic perturbations of…
On classification of higher rank Anosov actions on compact manifold
Danijela Damjanovic, Disheng Xu
We prove global smooth classification results for TNS totally Anosov Z^k actions on general compact manifolds, under each one of the following conditions: joint integrability, reso…
On conservative partially hyperbolic abelian actions with compact center foliation
Danijela Damjanovic, Disheng Xu
We consider smooth partially hyperbolic volume preserving Z^k actions on smooth manifolds, with uniformly compact center foliation. We show that under certain irreducibility condit…
Diffeomorphism group valued cocycles over higher rank abelian Anosov actions
Danijela Damjanovic, Disheng Xu
We prove that every smooth diffeomorphism group valued cocycle over certain abelian Anosov actions on tori (and more generally on infranilmanifolds), is a smooth coboundary on a fi…
Positivity of the top Lyapunov exponent for cocycles on semisimple Lie groups over hyperbolic bases
Mario Bessa, Jairo Bochi, Michel Cambrainha +3
A theorem of Viana says that almost all cocycles over any hyperbolic system have nonvanishing Lyapunov exponents. In this note we extend this result to cocycles on any noncompact c…
Uniformly quasiconformal partially hyperbolic systems
Clark Butler, Disheng Xu
We study smooth volume-preserving perturbations of the time-1 map of the geodesic flow of a closed Riemannian manifold of dimension at least three with constant negative cu…
Singular analytic linear cocycles with negative infinite Lyapunov exponents
Christian Sadel, Disheng Xu
We show that linear analytic cocycles where all Lyapunov exponents are negative infinite are nilpotent. For such one-frequency cocycles we show that they can be analytically conjug…
Density of positive Lyapunov exponents for symplectic cocycles
Disheng Xu
We prove that Sp(2d;R), HSp(2d) and pseudo unitary cocycles with at least one non-zero Lyapunov exponent are dense in all usual regularity classes for non periodic dynamical system…