3 papers
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 and all bounded type irrational , in the space of monic polynomials having a period Siegel disk of rotation number , the maximu…
math.DS2025
On the stability of holomorphic families of endomorphisms of
François Berteloot, Xavier Buff
In the context of holomorphic families of 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…