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Braverman and Yampolsky: Computability of Julia Sets

Algorithms and Computations in Mathematics, Volume 23, Springer

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References

  1. 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.

    Chapter  Google Scholar 

  2. 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.

    MathSciNet  MATH  Google Scholar 

  3. 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.

    Article  MATH  Google Scholar 

  4. X. Buff, A. Chéritat, Quadratic Julia sets with positive area, Ann. Math. (to appear).

  5. L. Carleson, T.W. Gamelin, Complex Dynamics. Universitext: Tracts in Mathematics (Springer, New York, 1993). ISBN 0-387-97942-5.

    MATH  Google Scholar 

  6. 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.

    Google Scholar 

  7. P. Fatou, Sur les substitutions rationnelles, C. R. Math. Acad. Sci. Paris 164, 806–808 (1917).

    MATH  Google Scholar 

  8. P. Fatou, Sur les substitutions rationnelles, C. R. Math. Acad. Sci. Paris 165, 992–995 (1917).

    Google Scholar 

  9. G. Julia, Mémoire sur l’iteration des fonctions rationnelles, J. Math. Pures Appl. 8, 47–245 (1918).

    Google Scholar 

  10. 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.

    Article  MathSciNet  MATH  Google Scholar 

  11. J. Milnor, Dynamics in One Complex Variable, 3rd edn. Annals of Mathematics Studies, vol. 160 (Princeton University Press, Princeton, 2006).

    MATH  Google Scholar 

  12. 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.

    MATH  Google Scholar 

  13. 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.

    Chapter  Google Scholar 

  14. D. Sullivan, Itération des fonctions analytiques complexes, C. R. Acad. Sci. Paris Ser. I Math. 294(9), 301–303 (1982). ISSN 0249-6321.

    MathSciNet  MATH  Google Scholar 

  15. 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.

    Article  MATH  Google Scholar 

  16. 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.

    MathSciNet  Google Scholar 

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Correspondence to Arnaud Chéritat.

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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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