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Discrete Holomorphic Local Dynamical Systems

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Dynamics of Entire Functions 339<br />

[Sch04b] Schleicher, D.: On fibers and local connectivity of Mandelbrot and Multibrot sets.<br />

In: M. Lapidus, M. van Frankenhuysen (eds.) Fractal Geometry and Applications:<br />

A Jubilee of Benoit Mandelbrot. Proceedings of Symposia in Pure Mathematics<br />

72, pp. 477–507. American Mathematical Society, Providence, RI (2004)<br />

[Sch07a] Schleicher, D.: Hausdorff dimension, its properties, and its surprises. Am. Math.<br />

Monthly 114(6), 509–528 (2007)<br />

[Sch07b] Schleicher, D. The dynamical fine structure of iterated cosine maps and a dimension<br />

paradox. Duke Math. J. 136(2), 343–356 (2007)<br />

[Sch08] Schleicher, D.: Newton’s method as a dynamical system: efficient root finding of<br />

polynomials and the Riemann ζ function. In: M. Lyubich, M. Yampolsky (eds.)<br />

<strong>Holomorphic</strong> Dynamics and Renormalization: a Volume in Honour of John Milnor’s<br />

75th birthday. Fields Institute Communications 53, 213–224 (2008)<br />

[SZ03a] Schleicher, D., Zimmer, J.: Escaping points for exponential maps. J. Lond. Math.<br />

Soc. (2) 67, 380–400 (2003)<br />

[SZ03b] Schleicher, D., Zimmer, J.: Periodic points and dynamic rays of exponential maps.<br />

Ann. Acad. Sci. Fenn. 28(2), 327–354 (2003)<br />

[Schu08] Schubert, H.: Area of Fatou sets of trigonometric functions. Proc. Am. Math. Soc.<br />

136, 1251–1259 (2008)<br />

[Se09] Selinger, N.: On the Boundary Behavior of Thurston’s Pullback Map. In:<br />

Dierk Schleicher (ed.) Complex Dynamics: Families and Friends, pp. 585–595,<br />

Chapter 16. A K Peters, Wellesley, MA (2009)<br />

[Sh87] Shishikura, M.: On the quasiconformal surgery of rational functions. Ann. Sci. Éc.<br />

Norm. Sup. 4e Ser. 20, 1–29 (1987)<br />

[Sh09] Shishikura, M.: The connectivity of the Julia set and fixed points. In: Dierk<br />

Schleicher (ed.) Complex Dynamics: Families and Friends, pp. 257–276.<br />

Chapter 6. A K Peters, Wellesley, MA (2009)<br />

[St96] Stallard, G.: The Hausdorff dimension of Julia sets of entire functions. II. Math.<br />

Proc. Cambridge Philos. Soc. 119(3), 513–536 (1996)<br />

[St97] Stallard, G.: The Hausdorff dimension of Julia sets of entire functions. III. J. Math.<br />

Proc. Camb. Philos. Soc. 122(2), 223–244 (1997)<br />

[St08] Stallard, G.: Dimensions of Julia sets of transcendental meromorphic functions. In:<br />

Transcendental dynamics and complex analysis, Lond. Math. Soc. Lecture Note<br />

Ser. 348, pp. 425–446. Cambridge University Press, Cambridge 2008<br />

[Ur03] Urbański, M.: Measures and dimensions in conformal dynamics. Bull. Am. Math.<br />

Soc. (N.S.) 40(3), 281–321 (2003)<br />

[UZ07] Urbański, M., Zdunik, A.: Instability of exponential Collet-Eckmann maps. Israel<br />

J. Math. 161, 347–371 (2007)<br />

[Tö39] Töpfer, H.: Über die Iteration der ganzen transzendenten Funktionen, insbesondere<br />

von sin z und cos z (German), Math. Ann. 117, 65–84 (1939)<br />

[Ye94] Ye, Z.: Structural instability of exponential functions. Trans. Am. Math. Soc.<br />

344(1), 379–389 (1994)<br />

[Y95] Yoccoz, J.-C.: Théorème de Siegel, nombres de Bruno et polynômes quadratiques.<br />

Petits diviseurs en dimension 1. Astérisque 231, 3–88 (1995)<br />

[Zh06] Zheng, J.-H.: On multiply-connected Fatou components in iteration of<br />

meromorphic functions. J. Math. Anal. Appl. 313(1), 24–37 (2006)<br />

[Z75] Zalcman, L.: A heuristic principle in complex function theory. Am. Math. Monthly<br />

82(8), 813–817 (1975)

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