6 citations · 20 across the 20 of their papers we have counts for
26 papers
An arithmetic approach to parabolic multiplicity in complex dynamics
Xavier Buff, Valentin Huguin, Liz Vivas
When is a primitive -th root of unity, the quadratic polynomial and the entire map both have a parabolic fixed point at . T…
Entire maps with rational preperiodic points and multipliers
Xavier Buff, Igors Gorbovickis, Valentin Huguin
Given a number field that is not contained in , we prove the existence of a dense set of entire maps $f \colon \mathbb{C} \rightarrow \m…
Introduction to Fatou components in holomorphic dynamics
Xavier Buff, Jasmin Raissy
This survey is an introduction to the classification of Fatou components in holomorphic dynamics. We start with the description of the Fatou and Julia sets for rational maps of the…
Entire or rational maps with integer multipliers
Xavier Buff, Thomas Gauthier, Valentin Huguin +1
Let be the ring of integers of an imaginary quadratic field . Recently, Ji and Xie proved that every rational map $f \colon \widehat{\mathbb{C}} \rightarrow \w…
Totally real points in the Mandelbrot Set
Xavier Buff, Sarah Koch
Recently, Noytaptim and Petsche proved that the only totally real parameters for which is postcritically finite are , and .…
Smooth Siegel disks everywhere
Artur Avila, Xavier Buff, Arnaud Chéritat
We prove the existence of Siegel disks with smooth boundaries in most families of holomorphic maps fixing the origin. The method can also yield other types of regularity conditions…