Title Dynamics in one complex variable / by John Milnor

Edition 3rd ed Published Princeton : Princeton University Press, 2006

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Description 1 online resource (viii, 304 pages) : illustrations Series Annals of mathematics studies ; no. 160 Annals of mathematics studies ; no. 160. Contents Riemann surfaces -- Iterated holomorphic maps -- Local fixed point theory -- Periodic points: global theory -- Structure of the Fatou set -- Using the Fatou set to study the Julia set Summary This volume studies the dynamics of iterated holomorphic mappings from a Riemann surface to itself, concentrating on the classical case of rational maps of the Riemann sphere. This subject is large and rapidly growing. These lectures are intended to introduce some key ideas in the field, and to form a basis for further study. The reader is assumed to be familiar with the rudiments of complex variable theory and of two-dimensional differential geometry, as well as some basic topics from topology. This third edition contains a number of minor additions and improvements: A historical survey has been added, the definition of Lattés map has been made more inclusive, and the écalle-Voronin theory of parabolic points is described. The résidu itératif is studied, and the material on two complex variables has been expanded. Recent results on effective computability have been added, and the references have been expanded and updated. Written in his usual brilliant style, the author makes difficult mathematics look easy. This book is a very accessible source for much of what has been accomplished in the field Bibliography Includes bibliographical references (pages 277-291) and index Notes In English Print version record Subject Functions of complex variables. Holomorphic mappings. Riemann surfaces. MATHEMATICS -- Complex Analysis. MATHEMATICS -- General. Functions of complex variables Holomorphic mappings Riemann surfaces Iterierte Abbildung Fixpunkttheorie Julia-Menge Fatou-Menge Riemannsche Fläche Holomorphe Abbildung Form Electronic book ISBN 9781400835539 1400835534 1283001489 9781283001489 9786613001481 6613001481

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