References
A.F. Beardon, Complex analytic dynamical systems, in Iteration of Rational Functions. Graduate Texts in Mathematics, vol. 132 (Springer, New York, 1991). ISBN 0-387-97589-6.
X. Buff, A. Chéritat, Ensembles de Julia quadratiques de mesure de Lebesgue strictement positive, C. R. Math. Acad. Sci. Paris 341(11), 669–674 (2005). ISSN 1631-073X. doi:10.1016/j.crma.2005.10.001.
X. Buff, A. Chéritat, The Brjuno function continuously estimates the size of quadratic Siegel disks, Ann. Math. 164(1), 265–312 (2006). ISSN 0003-486X. doi:10.4007/annals.2006.164.265.
X. Buff, A. Chéritat, Quadratic Julia sets with positive area, Ann. Math. (to appear).
L. Carleson, T.W. Gamelin, Complex Dynamics. Universitext: Tracts in Mathematics (Springer, New York, 1993). ISBN 0-387-97942-5.
A. Douady, Does a Julia set depend continuously on the polynomial? in Complex Dynamical Systems, Cincinnati, OH, 1994. Proc. Sympos. Appl. Math., vol. 49 (AMS, Providence, 1994), pp. 91–138.
P. Fatou, Sur les substitutions rationnelles, C. R. Math. Acad. Sci. Paris 164, 806–808 (1917).
P. Fatou, Sur les substitutions rationnelles, C. R. Math. Acad. Sci. Paris 165, 992–995 (1917).
G. Julia, Mémoire sur l’iteration des fonctions rationnelles, J. Math. Pures Appl. 8, 47–245 (1918).
S. Marmi, P. Moussa, J.-C. Yoccoz, The Brjuno functions and their regularity properties, Commun. Math. Phys. 186(2), 265–293 (1997). ISSN 0010-3616. doi:10.1007/s002200050110.
J. Milnor, Dynamics in One Complex Variable, 3rd edn. Annals of Mathematics Studies, vol. 160 (Princeton University Press, Princeton, 2006).
S. Morosawa, Y. Nishimura, M. Taniguchi, T. Ueda, Holomorphic Dynamics, Cambridge Studies in Advanced Mathematics, vol. 66 (Cambridge University Press, Cambridge, 2000). ISBN 0-521-66258-3. Translated from the 1995 Japanese original and revised by the authors.
N. Steinmetz, Complex analytic dynamical systems, in Rational Iteration. de Gruyter Studies in Mathematics, vol. 16 (Walter de Gruyter, Berlin, 1993). ISBN 3-11-013765-8.
D. Sullivan, Itération des fonctions analytiques complexes, C. R. Acad. Sci. Paris Ser. I Math. 294(9), 301–303 (1982). ISSN 0249-6321.
D. Sullivan, Quasiconformal homeomorphisms and dynamics. I. Solution of the Fatou–Julia problem on wandering domains, Ann. Math. 122(3), 401–418 (1985). ISSN 0003-486X. doi:10.2307/1971308.
J.-C. Yoccoz, Théorème de Siegel, nombres de Bruno et polynômes quadratiques, Astérisque 231, 3–88 (1995). ISSN 0303-1179. Petits diviseurs en dimension 1.
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Chéritat, A. Braverman and Yampolsky: Computability of Julia Sets. Found Comput Math 12, 123–137 (2012). https://doi.org/10.1007/s10208-011-9111-7
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DOI: https://doi.org/10.1007/s10208-011-9111-7