Dynamics in One Complex Variable

John Milnor - Collection Annals of Mathematic Studies

310 pages, parution le 27/02/2006 (3^eme édition)

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Résumé

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.

L'auteur - John Milnor

John Milnor is Professor of Mathematics and Co-Director of the Institute for Mathematical Sciences at SUNY, Stony Brook. He is the author of Topology from the Differential Viewpoint, Singular Points of Complex Hypersurfaces, Morse Theory, Introduction to Algebraic K-Theory, Characteristic Classes (with James Stasheff), and Lectures on the H-Cobordism Theorem (Princeton).

Sommaire

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

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	PAPIER
Éditeur(s)	Princeton University Press
Auteur(s)	John Milnor
Collection	Annals of Mathematic Studies
Parution	27/02/2006
Édition	3^eme édition
Nb. de pages	310
Format	17,5 x 25,5
Couverture	Broché
Poids	560g
Intérieur	Noir et Blanc
EAN13	9780691124889
ISBN13	978-0-691-12488-9