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Book review of: M. Braverman and M. Yampolsky, Computability of Julia sets. (English) Zbl 1276.00010

Review of [Zbl 1314.37033].

MSC:

00A17 External book reviews
37F50 Small divisors, rotation domains and linearization in holomorphic dynamics
37-02 Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory
03D15 Complexity of computation (including implicit computational complexity)
03D28 Other Turing degree structures
30D05 Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable
37F10 Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets
65E05 General theory of numerical methods in complex analysis (potential theory, etc.)

Citations:

Zbl 1314.37033
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Full Text: DOI

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. · Zbl 0742.30002
[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 . · Zbl 1082.37049 · doi:10.1016/j.crma.2005.10.001
[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 . · Zbl 1109.37040 · doi:10.4007/annals.2006.164.265
[4] X. Buff, A. Chéritat, Quadratic Julia sets with positive area, Ann. Math. (to appear). · Zbl 1228.37036
[5] L. Carleson, T.W. Gamelin, Complex Dynamics. Universitext: Tracts in Mathematics (Springer, New York, 1993). ISBN 0-387-97942-5. · Zbl 0782.30022
[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. · Zbl 0934.30023
[7] P. Fatou, Sur les substitutions rationnelles, C. R. Math. Acad. Sci. Paris 164, 806–808 (1917). · JFM 46.0519.02
[8] P. Fatou, Sur les substitutions rationnelles, C. R. Math. Acad. Sci. Paris 165, 992–995 (1917). · JFM 46.0520.01
[9] G. Julia, Mémoire sur l’iteration des fonctions rationnelles, J. Math. Pures Appl. 8, 47–245 (1918). · JFM 46.0520.06
[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 . · Zbl 0947.30018 · doi:10.1007/s002200050110
[11] J. Milnor, Dynamics in One Complex Variable, 3rd edn. Annals of Mathematics Studies, vol. 160 (Princeton University Press, Princeton, 2006). · Zbl 1085.30002
[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. · Zbl 0979.37001
[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. · Zbl 0773.58010
[14] D. Sullivan, Itération des fonctions analytiques complexes, C. R. Acad. Sci. Paris Ser. I Math. 294(9), 301–303 (1982). ISSN 0249-6321. · Zbl 0496.30016
[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 . · Zbl 0589.30022 · doi:10.2307/1971308
[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.
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