Complex Dynamics and Geometry (Smf/Ams Texts and Monographs, V. 10) - Cerveau, D, Kay, Leslie (2003)
ISBN 082183228X
Subject Differentiable dynamical systems; Geometry, Algebraic
Publisher American Mathematical Society
Publication Date 10/1/2003
Format Paperback (252 x 178 mm)
Language eng
Translator Leslie Kay
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 Supérieure 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.

Personal Details
Collection Status In Collection
Index 1144
Read It Yes
Links Amazon US
Product Details
LoC Classification QA614.8.D9613 2003
Dewey 514/.74
Cover Price $59.00
No. of Pages 197