Complex Dynamics and Geometry

American Mathem

ISBN 10: 082183228X / ISBN 13: 9780821832288

Published by American Mathematical Society, US, 2003

About this Item

In the last twenty years, the theory of holomorphic dynamical systems has had a resurgence of activity, particularly concerning the fine analysis of Julia sets associated with polynomials and rational maps in one complex variable. At the same time, closely related theories have had a similar rapid development, for example the qualitative theory of differential equations in the complex domain. The meeting, 'Etat de la recherche', held at Ecole Normale Superieure de Lyon, presented the current state of the art in this area, emphasizing the unity linking the various sub-domains. This volume contains four survey articles corresponding to the talks presented at this meeting. D. Cerveau describes the structure of polynomial differential equations in the complex plane, focusing on the local analysis in neighborhoods of singular points.E. Ghys surveys the theory of laminations by Riemann surfaces which occur in many dynamical or geometrical situations. N. Sibony describes the present state of the generalization of the Fatou-Julia theory for polynomial or rational maps in two or more complex dimensions. Lastly, the talk by J.-C. Yoccoz, written by M. Flexor, considers polynomials of degree $2$ in one complex variable, and in particular, with the hyperbolic properties of these polynomials centered around the Jakobson theorem. This is a general introduction that gives a basic history of holomorphic dynamical systems, demonstrating the numerous and fruitful interactions among the topics. In the spirit of the 'Etat de la recherche de la SMF' meetings, the articles are written for a broad mathematical audience, especially students or mathematicians working in different fields. This book is translated from the French edition by Leslie Kay.

Seller Inventory # LU-9780821832288

Bibliographic Details

• Title: Complex Dynamics and Geometry
• Publisher: American Mathematical Society, US
• Publication Date: 2003
• Language: English
• ISBN 10: 082183228X
• ISBN 13: 9780821832288
• Binding: Paperback
• Condition: New
• Weight: 369 grams

About this title

Synopsis

This work consists of four articles corresponding to lectures from a January 1997 meeting on the theory of holomorphic dynamical systems. Articles describe the structure of polynomial differential equations in the complex plane, examine the theory of laminations by Riemann surfaces which occur in many dynamical or geometrical situations, analyze the generalization of the Fatou-Julia theory for polynomials or rational maps in complex dimensions, and consider polynomials of degree 2 in one complex variable. The book was first published in French as Dynamique et Géométrie Complexes . Annotation (c) Book News, Inc., Portland, OR (booknews.com)