Yugang Zhang

activity

20232026

collaborators

7 papers

math.DS2026

A general endomorphism of $P^{k}$ has trivial iterated centralizer

Yugang Zhang

Fix integers $k, d \geq 2$ . Let $End_{d}^{k}$ denote the parameter space of endomorphisms of $P^{k}$ of algebraic degree $d$ . We prove that there exists a dense Zariski op…

math.DS2026

Measure rigidity for regular polynomial endomorphisms and applications

Yugang Zhang

We classify regular polynomial endomorphisms of $C^{k}$ with the same equilibrium measure under some mild condition on the dynamics at infinity. In particular, for $f$ in a Z…

math.DS2026

Special regular polynomial skew products

Yugang Zhang

We define a regular polynomial skew product $(p (z), q (z, w))$ of $C^{2}$ of degree $d \geq 2$ to be special if it is triangularly conjugate to a map of the form $(p (z), q (w))$ ,…

math.DS2026

Uniform bound on common periodic points for families of regular plane polynomial automorphisms

Marc Abboud, Yugang Zhang

Given two one-dimensional families $f$ and $g$ of regular plane polynomial automorphisms parameterised by an algebraic curve $B$ , all defined over some number field $K$ , such that…

math.DS2024

Marked points of families of hyperbolic automorphisms of smooth complex projective varieties

Yugang Zhang

Let $π : X \to Λ$ be a flat family of smooth complex projective varieties parameterized by a smooth quasi-projective variety $Λ$ , and let $f : X \to X$ be a family of automorphisms wit…

math.DS2024

Arithmetic properties of families of plane polynomial automorphisms

Yugang Zhang

Given an algebraic family $f : Λ \times A^{2} \to Λ \times A^{2}$ of plane polynomial automorphisms of Hénon type parameterized by a quasi-projective curve, defined…

math.AG2023

Gap for geometric canonical height functions

Yugang Zhang

We prove the existence of a gap around zero for canonical height functions associated to endomorphisms of projective spaces defined over complex function fields. We also prove that…

A general endomorphism of Pk has trivial iterated centralizer

Measure rigidity for regular polynomial endomorphisms and applications

Special regular polynomial skew products

Uniform bound on common periodic points for families of regular plane polynomial automorphisms

Marked points of families of hyperbolic automorphisms of smooth complex projective varieties

Arithmetic properties of families of plane polynomial automorphisms

Gap for geometric canonical height functions

A general endomorphism of $P^{k}$ has trivial iterated centralizer