Discrete Holomorphic Local Dynamical Systems
Discrete Holomorphic Local Dynamical Systems
Discrete Holomorphic Local Dynamical Systems
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
Dynamics of Entire Functions 337<br />
[FJT08] Fagella, N., Jarque, X., Taixés, J.: On connectivity of Julia sets of transcendental<br />
meromorphic maps and weakly repelling fixed points I. Proc. Lond. Math. Soc.<br />
97(3), 599–622 (2008)<br />
[Fa26] Fatou, P.: Sur l’itération des fonctions transcendantes entières. Acta Math. 47,<br />
337–370 (1926)<br />
[FS09] Förster, M., Schleicher, D.: Parameter rays in the space of exponential maps.<br />
Ergod. Theor. Dyn. Syst. 29, 515–544 (2009)<br />
[FRS08] Förster, M., Rempe, L., Schleicher, D.: Classification of escaping exponential<br />
maps. Proc. Am. Math. Soc. 136, 651–663 (2008)<br />
[Ge01] Geyer, L.: Siegel discs, Herman rings and the Arnold family. Trans. Am. Math.<br />
Soc. 353(9), 3661–3683 (2001)<br />
[GE79] Gol’dberg, A., Eremenko, A.: Asymptotic curves of entire functions of finite order.<br />
Mat. Sb. (N.S.) 109(151)(4), 555–581, 647 (1979)<br />
[GK86] Goldberg, L., Keen, L.: A finiteness theorem for a dynamical class of entire functions.<br />
Ergod. Theor. Dyn. Syst. 6, 183–192 (1986)<br />
[GKS04] Graczyk, J., Kotus, J., ´Swiátek, G.: Non-recurrent meromorphic functions. Fund.<br />
Math. 182(3), 269–281 (2004)<br />
[Gr18a] Gross, W.: Über die Singularitäten analytischer Funktionen. Monatsh. Math. Phys.<br />
29(1), 3–47 (1918)<br />
[Gr18b] Wilhelm, G.: Eine ganze Funktion, für die jede komplexe Zahl Konvergenzwert ist<br />
(German). Math. Ann. 79(1–2), 201–208 (1918)<br />
[Ha99] Haruta, M.: Newton’s method on the complex exponential function. Trans. Am.<br />
Math. Soc. 351(6), 2499–2513 (1999)<br />
[H64] Hayman, W.: Meromorphic Functions. Oxford Mathematical Monographs,<br />
Clarendon Press, Oxford (1964)<br />
[He57] Heins, M.: Asymptotic spots of entire and meromorphic functions. Ann. Math. (2)<br />
66, 430–439 (1957)<br />
[HSS09] Hubbard, J., Schleicher, D., Shishikura, M.: Exponential Thurston maps and limits<br />
of quadratic differentials. J. Am. Math. Soc. 22, 77–117 (2009)<br />
[Iv14] Iversen, F.: Recherches sur les fonctions inverses des fonctions méromorphes.<br />
Thèse, Helsingfors, 1914 (see [Ne53]).<br />
[Ka99] Karpińska, B.: Hausdorff dimension of the hairs without endpoints for λ exp(z).<br />
C. R. Acad. Sci. Paris Séer. I Math. 328, 1039–1044 (1999)<br />
[KU06] Karpińska, B., Urbański, M.: How points escape to infinity under exponential<br />
maps. J. Lond. Math. Soc. (2) 73(1), 141–156 (2006)<br />
[KK97] Keen, L., Kotus, J.: Dynamics of the family λ tanz. Conform. Geom. Dyn. 1,<br />
28–57 (1997)<br />
[KS08] Kisaka, M., Shishikura, M.: On multiply connected wandering domains of entire<br />
functions. In: Phil Rippon, Gwyneth Stallard (eds.) Transcendental Dynamics and<br />
Complex Analysis, London Math. Soc. Lecture Note Ser. 348, Cambridge University<br />
Press, Cambridge (2008)<br />
[LSV08] Laubner, B., Schleicher, D., Vicol, V.: A combinatorial classification of postsingularly<br />
preperiodic complex exponential maps. Discr. Cont. Dyn. Syst. 22(3),<br />
663–682 (2008)<br />
[LSW99] Letherman, S., Schleicher, D., Wood, R.: On the 3n+1-problem and holomorphic<br />
dynamics. Exp. Math. 8(3), 241–251 (1999)<br />
[Ma90] Mayer, J.: An explosion point for the set of endpoints of the Julia set of λ exp(z).<br />
Ergod. Theor. Dyn. Syst. 10(1), 177–183 (1990)<br />
[May] Mayer, S.: Newton’s Method for Entire Functions. Diplomarbeit, Technische<br />
Universität München (2002)<br />
[MS06] Mayer, S., Schleicher, D.: Immediate and virtual basins of Newton’s method for<br />
entire functions. Ann. Inst. Fourier (Grenoble) 56(2), 325–336 (2006)<br />
[Mc87] McMullen, C.: Area and Hausdorff dimension of Julia sets of entire functions.<br />
Trans. Am. Math. Soc. 300(1), 329–342 (1987)