3 citations · 4 across the 3 of their papers we have counts for
5 papers
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_…
Scaling Ratios and Triangles in Siegel Disks
Xavier Buff, Christian Henriksen
Let , where is a quadratic irrational. McMullen proved that the Siegel disk for is self-similar about the critical point. We give a lower bound for the…
Geometry of the Feigenbaum map
Xavier Buff
We show that the Feigenbaum-Cvitanovic equation can be interpreted as a linearizing equation, and the domain of analyticity of the Feigenbaum fixed point of renormalization as a ba…