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Yu-Gang Zhang

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Preprint Sep 2026

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

Fix integers $k,d\geq2$. Let $\operatorname{End}_d^k$ denote the parameter space of holomorphic endomorphisms of $\mathbb{P}^k$ of algebraic degree $d$. We prove that there exists a dense Zariski open subset $U_{d,k}\subset\operatorname{End}_d^k$, defined over $\mathbb{Q}$, such that, for every $f\in U_{d,k}(\mathbb{C}...

Yu-Gang Zhang · 0 citations

Preprint Aug 2026

Measure rigidity for regular polynomial endomorphisms and applications

We prove measure-rigidity results for regular polynomial endomorphisms of~$\mathbb{C}^k$. For maps of the same degree whose leading homogeneous parts differ by an invertible linear map on the target, equality of equilibrium measures is equivalent to postcomposition by an affine symmetry of the Julia set. We then show t...

Yu-Gang Zhang · 2 citations