6 papers · 1 filter
On the stability of rank-one factors for Anosov -actions
Danijela Damjanovic, Jiesong Zhang
We prove -stability of rank-one factors for a large class of higher rank Anosov -actions. If the factor is a projection of a smooth fiber bundle and th…
Invariant complex structures for affine automorphisms: a cocycle viewpoint
Jiesong Zhang
We prove that if a holomorphic diffeomorphism of a compact complex manifold is bi-Lipschitz conjugate to an ergodic affine automorphism on , then the conjugacy i…
Extremal distributions of partially hyperbolic systems: the Lipschitz threshold
Martin Leguil, Disheng Xu, Jiesong Zhang
We prove a sharp phase transition in the regularity of the extremal distribution for volume-preserving partially hyperbolic diffeomorphisms on closed $3…
Invariant distributions of partially hyperbolic systems: fractal graphs, excessive regularity, and rigidity
Disheng Xu, Jiesong Zhang
We introduce a novel approach linking fractal geometry to partially hyperbolic dynamics, revealing several new phenomena related to regularity jumps and rigidity. One key result de…
On holomorphic partially hyperbolic systems
Disheng Xu, Jiesong Zhang
We construct examples illustrating that dynamically-defined distributions of holomorphic diffeomorphisms on compact complex manifolds are not necessarily holomorphic in any open su…
On uniformly quasiconformal Anosov diffeomorphisms with two dimensional distributions
Jiesong Zhang
We prove that a transitive uniformly -quasiconformal Anosov diffeomorphism with a two-dimensional unstable distribution has a globally defined stable holonomy. As a corollary, w…