18 citations · 48 across the 13 of their papers we have counts for
13 papers
Location of Siegel capture polynomials in parameter spaces
Alexander Blokh, Arnaud Cheritat, Lex OVersteegen +1
A cubic polynomial with a periodic Siegel disk containing an eventual image of a critical point is said to be a \emph{Siegel capture polynomial}. If the Siegel disk is invarian…
A Proof of the Marmi-Moussa-Yoccoz conjecture for rotation numbers of high type
Davoud Cheraghi, Arnaud Chéritat
Marmi Moussa and Yoccoz conjectured that some error function Upsilon, related to the approximation of the size of Siegel disk by some arithmetic function of the rotation number the…
Herman's condition and critical points on the boundary of Siegel disks of polynomials with two critical values
Arnaud Chéritat, Pascale Roesch
We extend a theorem of Herman from the case of unicritical polynomials to the case of polynomials with two finite critical values. This theorem states that Siegel disks of such pol…
Relatively compact Siegel disks with non-locally connected boundaries
Arnaud Chéritat
We construct holomorphic maps with a Siegel disk whose boundary is not locally connected (and is an indecomposable continuum), yet compactly contained in the domain of definition o…
The solar Julia sets of basic quadratic Cremer polynomials
A. Blokh, X. Buff, A. Chéritat +1
In general, little is known about the exact topological structure of Julia sets containing a Cremer point. In this paper we show that there exist quadratic Cremer Julia sets of pos…
Quadratic Julia Sets with Positive Area
Xavier Buff, Arnaud Cheritat
We prove the existence of quadratic polynomials having a Julia set with positive Lebesgue measure in three cases: the presence of a Cremer fixed point, the presence of a Siegel dis…