3 citations · 7 across the 6 of their papers we have counts for
6 papers
Semi-continuity of Siegel disks under parabolic implosion
Arnaud Cheritat
We transfer the lower semi-continuity of Siegel disks with fixed Brjuno type rotation numbers to geometric limits. Here, we restrict to Lavaurs maps associated to quadratic polynom…
Ghys-like models providing trick for a class of simple maps
Arnaud Cheritat
For quadratic polynomials with an indifferent fixed point with bounded type rotation number (they have a Siegel disk), much of what is known of their Julia set comes from the study…
The measure of quadratic Julia-Lavaurs sets with a bounded type virtual Siegel disk is zero
Arnaud Cheritat
We prove here one of the claims of the author's thesis.
The Brjuno function continuously estimates the size of quadratic Siegel disks
Xavier Buff, Arnaud Cheritat
If alpha is an irrational number, we define Yoccoz's Brjuno function Phi by Phi(alpha)=sum_{n geq 0} alpha_0*alpha_1*...*alpha_{n-1}*log(1/alpha_n), where alpha_0 is the fractional…
Quadratic Siegel Disks with Rough Boundaries
Xavier Buff, Arnaud Cheritat
In the quadratic family (the set of polynomials of degree 2), Petersen and Zakeri proved the existence of Siegel disks whose boundaries are Jordan curves, but not quasicircles. In…
On the Size of Quadratic Siegel Disks: Part I
Xavier Buff, Arnaud Cheritat
If $\a$ is an irrational number, we let , be the approximants given by its continued fraction expansion. The Bruno series $B(\a)$ is defined as $$B(\a)=\sum_…