Renormalization and Geometry in One-Dime

Renormalization and Geometry in One-Dime
1 369,- 1 369,-
Format E-Bok
Filformat PDF
Utgivelsesår 1996
Forlag World Scientific Publishing Co
Språk Engelsk
ISBN 9789814350105
Sider 328
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Om Renormalization and Geometry in One-Dime

About one and a half decades ago, Feigenbaum observed that bifurcations, from simple dynamics to complicated ones, in a family of folding mappings like quadratic polynomials follow a universal rule (Coullet and Tresser did some similar observation independently) . This observation opened a new way to understanding transition from nonchaotic systems to chaotic or turbulent system in fluid dynamics and many other areas. The renormalization was used to explain this observed universality. This research monograph is intended to bring the reader to the frontier of this active research area which is concerned with renormalization and rigidity in real and complex one-dimensional dynamics. The research work of the author in the past several years will be included in this book. Most recent results and techniques developed by Sullivan and others for an understanding of this universality as well as the most basic and important techniques in the study of real and complex one-dimensional dynamics will also be included here.Contents:The Denjoy Distortion Principle and RenormalizationThe Koebe Distortion PrincipleThe Geometry of One-Dimensional MapsThe Renormalization Method and Folding MappingsThe Renormalization Method and Quadratic-Like MapsThermodynamical Formalism and the Renormalization OperatorReadership: Graduates and researchers in physics, mathematical physics and mathematics.Key Features:Give a systematical and all-round discussion on the subject matterThe author has made many contributions on partial differential equations and microlocal analysis. He is one of the invited speakers of ICM2010


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