3 papers
math.DS2026
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…
math.DS2024
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…
math.DS2024
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…