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.DS2025
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…
math.DS2025
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…