Dynamics of Entire Functions 335 References [AO93] Aarts, J.M., Oversteegen, L.G.: The geometry of Julia sets. Trans. Am. Math. Soc. 338(2), 897–918 (1993) [Ab] Abate, M.: <strong>Discrete</strong> holomorphic local dynamical systems, course notes, this volume [A98] Ahlfors, L.: Complex analysis, 3rd edn. International Series in Pure and Applied Mathematics. McGraw-Hill Book Co., New York (1978) [BBS08] Bailesteanu, M., Balan, V., Schleicher, D.: Hausdorff dimension of exponential parameter rays and their endpoints. Nonlinearity 21(1), 113–120 (2008) [Ba60] Baker, I.N.: The existence of fixpoints of entire functions. Math. Zeitschr. 73, 280– 284 (1960) [Ba63] Baker, I.N.: Multiply connected domains of normality in iteration theory. Math. Z. 81, 206–214 (1963) [Ba76] Baker, I.N.: An entire function which has wandering domains. J. Austral. Math. Soc. Ser. A 22(2), 173–176 (1976) [Ba81] Baker, I.N.: The iteration of polynomials and transcendental entire functions. J. Austral. Math. Soc. Ser. A 30, 483–495 (1980/81) [Ba84] Baker, I.N.: Wandering domains in the iteration of entire functions. Proc. Lond. Math. Soc. (3) 49(3), 563–576 (1984) [BKL91] Baker, I.N., Kotus, J., Lü, Y.N.: Iterates of meromorphic functions. III. Preperiodic domains. Ergod. Theor. Dyn. Syst. 11(4), 603–618 (1991) [BR84] Baker, I.N., Rippon, P.: Iteration of exponential functions. Ann. Acad. Sci. Fenn. Ser. A I Math. 9, 49–77 (1984) [Bar07] Barański, K.: Trees and hairs for some hyperbolic entire maps of finite order. Math. Z. 257(1), 33–59 (2007) [Bar08] Barański, K.: Hausdorff dimension of hairs and ends for entire maps of finite order. Math. Proc. Cambridge Philos. Soc. 145(3), 719–737 (2008) [Ben] Benini, A.: Combinatorial rigidity for Misiurewicz parameters. Manuscript, in preparation. [Ba99] Bargmann, D.: Simple proofs of some fundamental properties of the Julia set. Ergod. Theor. Dyn. Syst. 19(3), 553–558 (1999) [Ba01] Bargmann, D.: Normal families of covering maps. J. Analyse. Math. 85, 291–306 (2001) [BB01] Bargmann, D., Bergweiler, W.: Periodic points and normal families. Proc. Am. Math. Soc. 129(10), 2881–2888 (2001) [BD00] Berteloot, F., Duval, J.: Une démonstration directe de la densité des cycles répulsifs dans l’ensemble de Julia. Progr. Math. 188, Birkhäuser, Basel, 221–222 (2000) [Be91] Bergweiler, W.: Periodic points of entire functions: proof of a conjecture of Baker. Complex Variables Theory Appl. 17, 57–72 (1991) [Be93] Bergweiler, W.: Iteration of meromorphic functions. Bull. Am. Math. Soc. (N.S.) 29(2), 151–188 (1993) [Be] Bergweiler, W.: An entire function with simply and multiply connected wandering domains, to appear in Pure Appl. Math. Quarterly [Be98] Bergweiler, W.: A new proof of the Ahlfors five islands theorem. J. Anal. Math. 76, 337–347 (1998) [BDL07] Bergweiler, W., Drasin, D., Langley, J.K.: Baker domains for Newton’s method. Ann. Inst. Fourier (Grenoble) 57(3), 803–814 (2007) [BE95] Bergweiler, W., Eremenko, A.: On the singularities of the inverse to a meromorphic function of finite order. Rev. Mat. Iberoamericana 11(2), 355–373 (1995) [BHKMT93] Bergweiler, W., Haruta, M., Kriete, H., Meier, H., Terglane, N.: On the limit functions of iterates in wandering domains. Ann. Acad. Sci. Fenn. Ser. A I Math. 18(2), 369–375 (1993)
336 Dierk Schleicher [BH99] Bergweiler, W., Hinkkanen, A.: On semiconjugation of entire functions. Math. Proc. Cambridge Philos. Soc. 126(3), 565–574 (1999) [BKS] Bergweiler, W., Karpińska, B., Stallard, G.: The growth rate of an entire function and the Hausdorff dimension of its Julia set. J. Lond. Math. Soc., doi:10.1112/jlms/jdp042 [BT96] Bergweiler, W., Terglane, N.: Weakly repelling fixpoints and the connectivity of wandering domains. Trans. Am. Math. Soc. 348(1), 1–12 (1996) [BRS08] Bergweiler, W., Rippon, P., Stallard, G.: Dynamics of meromorphic functions with direct or logarithmic singularities. Proc. Lond. Math. Soc. 97, 368-400 (2008) [Bo96] Bock, H.: On the dynamics of entire functions on the Julia set. Results Math. 30(1– 2), 16–20 (1996) [BS] Bruin, H., Kaffl, A., Schleicher, D.: Symbolic Dynamcis of Quadratic Polynomials. Monograph, in preparation. Earlier version: Mittag-Leffler Preprint 7 (2001/02) [BR06] Buff, X., Rückert, J.: Virtual immediate basins of Newton maps and asymptotic values. Int. Math. Res. Not., Art. ID 65498, 18 (2006) [DGH] Devaney, R., Goldberg, L., Hubbard, J.: A dynamical approximation to the exponential map of polynomials. Preprint, MSRI (1986). See [BDGHHR99]. [BDGHHR99] Bodelon, C., Devaney, R., Goldberg, L., Hayes, M., Hubbard, J., Roberts, G.: Hairs for the complex exponential family. Internat. J. Bif. Chaos 9(8), 1517–1534 (1999) [DK84] Devaney, R., Krych, M.: Dynamics of exp(z). Ergod. Theor. Dyn. Syst. 4(1), 35–52 (1984) [DT86] Devaney, R., Tangerman, F.: Dynamics of entire functions near the essential singularity. Ergod. Theor. Dyn. Syst. 6(4), 489–503 (1986) [DFJ02] Devaney, R., Fagella, N., Jarque, X.: Hyperbolic components of the complex exponential family. Fund. Math. 174(3), 193–215 (2002) [Do98] Domínguez, P.: Dynamics of transcendental meromorphic functions. Annales Academiæ Scientiarum Fennicæ, Mathematica 23, 225–250 (1998) [DH93] Douady, A., Hubbard, J.: A proof of Thurston’s topological characterization of rational functions. Acta Math. 171, 263–297 (1993) [Ep] Epstein, A.: Infinitesimal thurston rigidity and the fatou-shishikura inequality. Stony Brook IMS preprint 1 (1999) [Er78] Eremenko, A.: The set of asymptotic values of a finite order meromorphic function (Russian). Mat. Zametki 24(6), 779–783, 893 (1978). (English translation: Math. Notes 24(5–6), 914–916 (1978)) [Er89] Eremenko, A.: On the iteration of entire functions. Banach Center Publ. 23,PWN, Warsaw, 339–345 (1989) [EL84a] Eremenko, A., Lyubich, M.: Iterates of entire functions. Soviet Math. Dokl. 30(3), 592–594 (1984) [EL84b] Eremenko, A., Lyubich, M.: Iterates of entire functions (Russian). Preprint, Institute for Low Temperature, Kharkov 6 (1984) [EL87] Eremenko, A., Lyubich, M.: Examples of entire functions with pathological dynamics. J. Lond. Math. Soc. 36, 458–468 (1987) [EL89] Eremenko, A., Lyubich, M.: The dynamics of analytic transformations (Russian). Algebra i Analiz 1(3), 1–70 (1989); translation in Leningrad Math. J. 1(3), 563–634 (1990) [EL92] Eremenko, A., Lyubich, M.: <strong>Dynamical</strong> properties of some classes of entire functions. Annales Inst. Fourier 42(4), 989–1020 (1992) [E1777] Euler, L.: De formulis exponentialibus replicatis. Acta Acad. Petropolitanae, 1, 38–60 (1777) [Fa99] Fagella, N.: Dynamics of the complex standard family. J. Math. Anal. Appl. 229(1), 1–31 (1999) [FaGa07] Fagella, N., Garijo, A.: The parameter planes of λ z m exp(z) for m ≥ 2. Comm. Math. Phys. 273(3), 755–783 (2007)
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Lecture Notes in Mathematics 1998 E
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Marco Abate · Eric Bedford · Marc
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Preface The theory of holomorphic d
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x Contents 2.7 Cremona Representati
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