Discrete Holomorphic Local Dynamical Systems

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Dynamics of Entire Functions 339 [Sch04b] Schleicher, D.: On fibers and local connectivity of Mandelbrot and Multibrot sets. In: M. Lapidus, M. van Frankenhuysen (eds.) Fractal Geometry and Applications: A Jubilee of Benoit Mandelbrot. Proceedings of Symposia in Pure Mathematics 72, pp. 477–507. American Mathematical Society, Providence, RI (2004) [Sch07a] Schleicher, D.: Hausdorff dimension, its properties, and its surprises. Am. Math. Monthly 114(6), 509–528 (2007) [Sch07b] Schleicher, D. The dynamical fine structure of iterated cosine maps and a dimension paradox. Duke Math. J. 136(2), 343–356 (2007) [Sch08] Schleicher, D.: Newton’s method as a dynamical system: efficient root finding of polynomials and the Riemann ζ function. In: M. Lyubich, M. Yampolsky (eds.) <strong>Holomorphic</strong> Dynamics and Renormalization: a Volume in Honour of John Milnor’s 75th birthday. Fields Institute Communications 53, 213–224 (2008) [SZ03a] Schleicher, D., Zimmer, J.: Escaping points for exponential maps. J. Lond. Math. Soc. (2) 67, 380–400 (2003) [SZ03b] Schleicher, D., Zimmer, J.: Periodic points and dynamic rays of exponential maps. Ann. Acad. Sci. Fenn. 28(2), 327–354 (2003) [Schu08] Schubert, H.: Area of Fatou sets of trigonometric functions. Proc. Am. Math. Soc. 136, 1251–1259 (2008) [Se09] Selinger, N.: On the Boundary Behavior of Thurston’s Pullback Map. In: Dierk Schleicher (ed.) Complex Dynamics: Families and Friends, pp. 585–595, Chapter 16. A K Peters, Wellesley, MA (2009) [Sh87] Shishikura, M.: On the quasiconformal surgery of rational functions. Ann. Sci. Éc. Norm. Sup. 4e Ser. 20, 1–29 (1987) [Sh09] Shishikura, M.: The connectivity of the Julia set and fixed points. In: Dierk Schleicher (ed.) Complex Dynamics: Families and Friends, pp. 257–276. Chapter 6. A K Peters, Wellesley, MA (2009) [St96] Stallard, G.: The Hausdorff dimension of Julia sets of entire functions. II. Math. Proc. Cambridge Philos. Soc. 119(3), 513–536 (1996) [St97] Stallard, G.: The Hausdorff dimension of Julia sets of entire functions. III. J. Math. Proc. Camb. Philos. Soc. 122(2), 223–244 (1997) [St08] Stallard, G.: Dimensions of Julia sets of transcendental meromorphic functions. In: Transcendental dynamics and complex analysis, Lond. Math. Soc. Lecture Note Ser. 348, pp. 425–446. Cambridge University Press, Cambridge 2008 [Ur03] Urbański, M.: Measures and dimensions in conformal dynamics. Bull. Am. Math. Soc. (N.S.) 40(3), 281–321 (2003) [UZ07] Urbański, M., Zdunik, A.: Instability of exponential Collet-Eckmann maps. Israel J. Math. 161, 347–371 (2007) [Tö39] Töpfer, H.: Über die Iteration der ganzen transzendenten Funktionen, insbesondere von sin z und cos z (German), Math. Ann. 117, 65–84 (1939) [Ye94] Ye, Z.: Structural instability of exponential functions. Trans. Am. Math. Soc. 344(1), 379–389 (1994) [Y95] Yoccoz, J.-C.: Théorème de Siegel, nombres de Bruno et polynômes quadratiques. Petits diviseurs en dimension 1. Astérisque 231, 3–88 (1995) [Zh06] Zheng, J.-H.: On multiply-connected Fatou components in iteration of meromorphic functions. J. Math. Anal. Appl. 313(1), 24–37 (2006) [Z75] Zalcman, L.: A heuristic principle in complex function theory. Am. Math. Monthly 82(8), 813–817 (1975)
List of Participants 1. Abate Marco, Italy, abate@dm.unipi.it 2. Arosio Leandro, Italy, arosio@mat.uniroma1.it 3. Bayraktar Turgay, USA, tbayrakt@indiana.edu 4. Bedford Eric, USA, bedford@indiana.edu 5. Bisi Cinzia, Italy, bisi@mat.unical.it 6. Brunella Marco, France, Marco.Brunella@u-bourgogne.fr 7. Cannizzo Jan, Germany, j.cannizzo@jacobs-university.de 8. Casavecchia Tiziano, Italy, casavecc@mail.dm.unipi.it 9. Corvaja Pietro, Italy, corvaja@dimi.uniud.it 10. de Fabritiis Chiara, Italy, fabritiis@dipmat.univpm.it 11. Deserti Julie, France, deserti@math.jussieu.fr 12. Dini Gilberto, Italy, dini@math.unifi.it 13. Francaviglia Stefano, Italy, s.francaviglia@sns.it 14. Frosini Chiara, Italy, frosini@math.unifi.it 15. Gentili Graziano, Italy, gentili@math.unifi.it 341
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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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Preface vii here are of independent
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x Contents 2.7 Cremona Representati
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List of Contributors Marco Abate Di
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2 Marco Abate on U ∩ f −1 (U) o
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4 Marco Abate without constant term
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6 Marco Abate Proof. Let us assume
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8 Marco Abate Definition 2.8. The n
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10 Marco Abate Then it is easy to c
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12 Marco Abate When |w| is so large
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14 Marco Abate As a consequence, th
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16 Marco Abate where β is a formal
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18 Marco Abate a lower half-plane.
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20 Marco Abate Definition 3.19. The
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22 Marco Abate Remark 4.5. The same
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24 Marco Abate Remark 4.11. Conditi
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26 Marco Abate defined for |t| smal
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28 Marco Abate � � � card 0
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30 Marco Abate to show (see, e.g.,
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32 Marco Abate Theorem 4.24 (Naishu
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34 Marco Abate it escapes both in f
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36 Marco Abate as I know, the probl
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38 Marco Abate 6 Several Complex Va
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40 Marco Abate Remark 6.8. There ar
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42 Marco Abate (ii) f |M is holomor
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44 Marco Abate In [ABT1] we proved
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46 Marco Abate and dimE = 1; but th
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48 Marco Abate It turns out that σ
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50 Marco Abate and the eigenvalues
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52 Marco Abate [CD] Coman, D., Dabi
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54 Marco Abate [Ni] Nishimura, Y.:
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Dynamics of Rational Surface Automo
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Uniformisation of Foliations by Cur
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166 Tien-Cuong Dinh and Nessim Sibo
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Page 307 and 308: 298 Dierk Schleicher In a brief app
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Page 331 and 332: 322 Dierk Schleicher 5 Hausdorff Di
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Page 339 and 340: 330 Dierk Schleicher Definition 7.1
Page 341 and 342: 332 Dierk Schleicher Conjecture 7.1
Page 343 and 344: 334 Dierk Schleicher Remark 8.13. T
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Discrete Holomorphic Local Dynamical Systems

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