Publications, preprints, and other documents
Other presentation :
array
.
Theses, reports
Exposé
de fin de 1ère année à l'ENS. :
Le spectre d'une variété riemannienne
(with Laurent Berger )
Mémoire de DEA
:
Petites copies de l'ensemble de Mandelbrot dans les éléphants
Thèse
, Orsay, décembre 2001 :
Recherche d'ensembles de Julia de mesure de Lebesgue positive
" :
Errata
Addendum à la thèse
:
Cage de Faraday
Mémoire
d'habiliation à diriger des recherches :
Sur l'implosion parabolique, la taille des disques de Siegel & une conjecture de Marmi, Moussa et Yoccoz
Prepublications or arXiv
Orsay, n° 99-77, 1999 :
Estimates on the speed of explosion of the parabolic fixed points of quadratic polynomials and applications
Toulouse III, n°242, mai 2002 :
Quadratic Siegel disks with smooth boundaries
(with Xavier Buff )
Toulouse III, n°267, mai 2003 (arXiv math.DS/0305080) :
On the size of quadratic Siegel disks. Part I
(with Xavier Buff )
arXiv math.DS/0309067 :
Quadratic Siegel disks with rough boundaries
(with Xavier Buff )
arXiv math.DS/0409384 :
The measure of quadratic Julia-Lavaurs sets with a bounded type virtual Siegel disk is zero
arXiv math.DS/0410003 :
Ghys-like models providing trick for a class of simple maps
arXiv math.DS/0507250 :
Semi-continuity of Siegel disks under parabolic implosion
arXiv math.DS/0604470 :
A new proof of a conjecture of Yoccoz, Remarks, New results
(with Xavier Buff )
arXiv math.DS/0605514 :
Quadratic Julia Sets with Positive Area
(with Xavier Buff )
arXiv:0812.1239 :
The solar Julia sets of basic quadratic Cremer polynomials
(with Xavier Buff , Alexander Blokh , Lex Oversteegen )
arXiv:0811.2601 :
Beltrami forms, affine surfaces and the Schwarz-Christoffel formula: a worked out example of straightening
arXiv:0906.1048 :
Relatively compact Siegel disks with non-locally connected boundaries
arXiv:1111.4629 :
Herman's condition and Siegel disks of polynomials
(with Pascale Roesch)
arXiv:1202.4188 :
Tan Lei and Shishikura's example of non-mateable degree 3 polynomials without a Levy cycle
arXiv:1210.5384 :
A Proof of the Marmi-Moussa-Yoccoz conjecture for rotation numbers of high type
(with Davoud Cheraghi )
arXiv:1311.7520 (math.CV) :
Proof of a convergence of affine Riemann surfaces to a richer one
arXiv:1701.03276 :
Generic 1-parameter pertubations of a vector field with a singular point of codimension k
(with Christiane Rousseau)
arXiv:1809.02586 :
Location of Siegel capture polynomials in parameter spaces
(with Alexander Blokh, Lex Oversteegen, Vladlen Timorin)
arXiv:1911.10056 :
Smooth Siegel disks everywhere
(with Artur Ávila, Xavier Buff)
arXiv:2003.13337 :
On the size of Siegel disks with fixed multiplier for cubic polynomials
arXiv:2212.12614 :
Similarity surfaces, connections, and the measurable Riemann mapping theorem
(with Guillaume Tahar)
arXiv:2302.12543 :
Stiff connections in pseudo-Euclidean manifolds
(with Guillaume Tahar)
Publications and submited articles
Acta Mathematica, 2004, [Vol. 193, pp 1-30]
(with Artur Avila, Xavier Buff)
Siegel disks with smooth boundaries
Comptes Rendus Mathématiques, 2002, [n°334/12, pp. 1107-1112]
Sur la vitesse d'explosion des points fixes paraboliques dans la famille quadratique
Inventiones Mathematicae, april 2004, [Vol. 156/1, pp. 1-24].
(with Xavier Buff)
Upper bound for the size of quadratic Siegel disks
Conformal Geometry & Dynamics, 2006 [Vol 10, pp. 227-256]
Ghys-like models for Lavaurs and simple entire maps
Proceedings of the AMS, 2007 [Vol 135, pp. 1073-1080]
(with Xavier Buff)
How regular can the boundary of a quadratic Siegel disk be?
Annals of Mathematics, 2006 [Vol 164/1, pp. 265-312]
(with Xavier Buff)
The Brjuno Function Continuously Estimates the Size of Siegel Disks
Comptes Rendus Mathématiques, 2004, [n°338/4, pp. 301-304]
Une nouvelle preuve d'un théorème de Yoccoz
Dynamics on the Riemann Sphere (a Bodil Branner Festschrift), EMS, 2006
Parabolic explosion and the size of Siegel disks in the quadratic family
Comptes Rendus Mathématiques, 2005, [n°341/11, pp. 669-674]
(with Xavier Buff)
Ensembles de Julia quadratiques de mesure de Lebesgue strictement positive
Ergodic Theory and Dynamical Systems, 2010, [volume 30, issue 01, pp. 51-65]
(with Xavier Buff, Alexander Blokh, Lex Oversteegen)
The solar Julia sets of basic quadratic Cremer polynomials
Annals of Mathematics, 2012, [Volume 176, issue 2, pp. 673-746]
(with Xavier Buff)
Quadratic Julia sets with positive area
Book: "Complex Dynamics, Families and Friends" 2009 [Editor: Dierk Schleicher, Publisher: AK Peters]
The hunt for Julia sets with positive measure
Mathematische Annalen, 2011 [Volume 349, Issue 3, pp. 529-542]
Relatively compact Siegel disks with non-locally connected boundaries
Annales de l'institut Fourier, 2011 [61 no. 1, pp. 319-350, doi: 10.5802/aif.2603]
(with Xavier Buff)
A new proof of a conjecture of Yoccoz
Annales de la Faculté des Sciences de Toulouse, Mathématiques 2012 [Série 6, Vol. 21, no. 5, pp. 935-980]
Tan Lei and Shishikura's example of non-mateable degree 3 polynomials without a Levy cycle.
Comptes Rendus Mathématiques 2015 [Vol. 353, no. 8, pp. 711-715]
(with Gao Yan, Ou Yafei, Tan Lei)
A refinement of the Gauss-Lucas theorem (after W. P. Thurston)
Inventiones Mathematicae 2015 [Vol. 202, no. 2, pp. 677-742]
(with Davoud Cheraghi)
A proof of the Marmi-Moussa-Yoccoz conjecture for rotation numbers of high type
Communications in Mathematical Physics 2016 [Vol. 344, no. 2, pp. 397-426]
(with Pascale Roesch)
Herman’s condition and Siegel disks of bi-critical polynomials
Science China. Mathematics 2018 [Vol. 61, no. 12, pp. 2139–2156]
(with Adam Epstein)
Bounded type Siegel disks of finite type maps with few singular values.
In Astérisque 416 (2020)
Some aspects of the theory of dynamical systems: a tribute to Jean-Christophe Yoccoz, Volume II
(with Artur Ávila, Xavier Buff)
Smooth Siegel disks everywhere
Nonlinearity (2021) [Volume 34, Number 4]
(with Alexander Blokh, Lex Oversteegen, Vladlen Timorin)
Location of Siegel capture polynomials in parameter spaces
Arnold Mathematical Journal (2022) [Vol. 8, no. 2, pp. 169–270].
Near parabolic renormalization for unicritical holomorphic maps
Reviews
SMF, 200? [Volume ?] :
The Mandelbrot Set, Theme and Variations
Foundations of Computational Mathematics: Volume 12, Issue 1 (2012), Page 123-137 :
Braverman and Yampolsky: Computability of Julia Sets
Others
Article
:
Fractions rationnelles associatives et corps quadratiques
