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arXiv · 2411.12856

Independence of multipliers in several variables complex dynamics

Igors Gorbovickis·Johan Taflin
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Abstract

We establish the independence of multipliers for polynomial endomorphisms of $\mathbb C^n$ and endomorphisms of $\mathbb P^n.$ This allows us to extend results about the bifurcation measure and the critical height obtained in \cite{arXiv:2305.02246} to the case of polynomial endomorphisms of $\mathbb C^n$ for $n\geq 3$. An important step in the proof is the irreducibility of the spaces of endomorphisms with $N$ marked periodic points, which is of independent interest.

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Igors Gorbovickis, Johan Taflin. 2025-01-08. Independence of multipliers in several variables complex dynamics. https://arxiv.org/abs/2411.12856

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