Discrete Holomorphic Local Dynamical Systems

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C.I.M.E. means Centro Internazionale Matematico Estivo, that is, International Mathematical Summer Center. Conceived in the early fifties, it was born in 1954 and made welcome by the world mathematical community where it remains in good health and spirit. Many mathematicians from all over the world have been involved in a way or another in C.I.M.E.’s activities during the past years. So they already know what the C.I.M.E. is all about. For the benefit of future potential users and co-operators the main purposes and the functioning of the Centre may be summarized as follows: every year, during the summer, Sessions (three or four as a rule) on different themes from pure and applied mathematics are offered by application to mathematicians from all countries. Each session is generally based on three or four main courses (24−30 hours over a period of 6−8 working days) held from specialists of international renown, plus a certain number of seminars. A C.I.M.E. Session, therefore, is neither a Symposium, nor just a School, but maybe a blend of both. The aim is that of bringing to the attention of younger researchers the origins, later developments, and perspectives of some branch of live mathematics. The topics of the courses are generally of international resonance and the participation of the courses cover the expertise of different countries and continents. Such combination, gave an excellent opportunity to young participants to be acquainted with the most advanced research in the topics of the courses and the possibility of an interchange with the world famous specialists. The full immersion atmosphere of the courses and the daily exchange among participants are a first building brick in the edifice of international collaboration in mathematical research. C.I.M.E. Director C.I.M.E. Secretary Pietro ZECCA Elvira MASCOLO Dipartimento di Energetica “S. Stecco” Dipartimento di Matematica “U. Dini” Università di Firenze Università di Firenze Via S. Marta, 3 viale G.B. Morgagni 67/A 50139 Florence 50134 Florence Italy Italy e-mail: zecca@unifi.it e-mail: mascolo@math.unifi.it For more information see CIME’s homepage: http://www.cime.unifi.it CIME activity is carried out with the collaboration and financial support of: – INdAM (Istituto Nationale di Alta Mathematica) – MIUR (Ministero dell’Universit e della Ricerca) This course is partially supported by LAMI (Laboratorio di Applicazioni della Matematica all’Ingegneria, Università della Calabria)
Marco Abate · Eric Bedford · Marco Brunella Tien-Cuong Dinh · Dierk Schleicher Nessim Sibony Holomorphic Dynamical Systems Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 7–12, 2008 Editors: Graziano Gentili Jacques Guenot Giorgio Patrizio 123
Page 1: Lecture Notes in Mathematics 1998 E
Page 5 and 6: Preface The theory of holomorphic d
Page 7 and 8: Preface vii here are of independent
Page 9 and 10: x Contents 2.7 Cremona Representati
Page 11 and 12: List of Contributors Marco Abate Di
Page 13 and 14: 2 Marco Abate on U ∩ f −1 (U) o
Page 15 and 16: 4 Marco Abate without constant term
Page 17 and 18: 6 Marco Abate Proof. Let us assume
Page 19 and 20: 8 Marco Abate Definition 2.8. The n
Page 21 and 22: 10 Marco Abate Then it is easy to c
Page 23 and 24: 12 Marco Abate When |w| is so large
Page 25 and 26: 14 Marco Abate As a consequence, th
Page 27 and 28: 16 Marco Abate where β is a formal
Page 29 and 30: 18 Marco Abate a lower half-plane.
Page 31 and 32: 20 Marco Abate Definition 3.19. The
Page 33 and 34: 22 Marco Abate Remark 4.5. The same
Page 35 and 36: 24 Marco Abate Remark 4.11. Conditi
Page 37 and 38: 26 Marco Abate defined for |t| smal
Page 39 and 40: 28 Marco Abate � � � card 0
Page 41 and 42: 30 Marco Abate to show (see, e.g.,
Page 43 and 44: 32 Marco Abate Theorem 4.24 (Naishu
Page 45 and 46: 34 Marco Abate it escapes both in f
Page 47 and 48: 36 Marco Abate as I know, the probl
Page 49 and 50: 38 Marco Abate 6 Several Complex Va
Page 51 and 52: 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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166 Tien-Cuong Dinh and Nessim Sibo
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296 Dierk Schleicher made possible
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298 Dierk Schleicher In a brief app
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300 Dierk Schleicher of f are discr
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302 Dierk Schleicher set with at le
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304 Dierk Schleicher logarithmic si
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306 Dierk Schleicher According to M
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308 Dierk Schleicher Theorem 2.1 (C
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310 Dierk Schleicher that each f (
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312 Dierk Schleicher An, weuseaC
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314 Dierk Schleicher The following
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316 Dierk Schleicher Fig. 1 The wig
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318 Dierk Schleicher Examples of Fa
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320 Dierk Schleicher 8. if f has a
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322 Dierk Schleicher 5 Hausdorff Di
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324 Dierk Schleicher centered annul
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326 Dierk Schleicher One way to int
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328 Dierk Schleicher indifferent or
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330 Dierk Schleicher Definition 7.1
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332 Dierk Schleicher Conjecture 7.1
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334 Dierk Schleicher Remark 8.13. T
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336 Dierk Schleicher [BH99] Bergwei
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338 Dierk Schleicher [Mi06] Milnor,
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List of Participants 1. Abate Marco
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Lecture Notes in Mathematics For in
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Vol. 1911: A. Bressan, D. Serre, M.
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LECTURE NOTES IN MATHEMATICS Edited
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Discrete Holomorphic Local Dynamical Systems

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