Xavier Buff

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20142026

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math.DS2026

Biggest bounded type Siegel disks of monic polynomials include those that stick to all critical points

Xavier Buff, Arnaud Chéritat, Pascale Roesch

We prove that for all degree $d \geq 2$ and all bounded type irrational $θ$ , in the space of monic polynomials having a period $1$ Siegel disk $Δ$ of rotation number $θ$ , the maximu…

math.DS2025

On the stability of holomorphic families of endomorphisms of $P^{k}$

François Berteloot, Xavier Buff

In the context of holomorphic families of $P^{k}$ endomorphisms, we show that various notions of stability are equivalent. This allows us to both extend and simplify the ar…

math.DS2014

A two-dimensional polynomial mapping with a wandering Fatou component

Matthieu Astorg, Xavier Buff, Romain Dujardin +2

We show that there exist polynomial endomorphisms of C^2, possessing a wandering Fatou component. These mappings are polynomial skew-products, and can be chosen to extend holomorph…

Biggest bounded type Siegel disks of monic polynomials include those that stick to all critical points

On the stability of holomorphic families of endomorphisms of Pk

A two-dimensional polynomial mapping with a wandering Fatou component

On the stability of holomorphic families of endomorphisms of $P^{k}$