Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics

One-Dimensional Dynamics

Authors: Melo, Welington de, Strien, Sebastian van

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About this book

One-dimensional dynamics has developed in the last decades into a subject in its own right. Yet, many recent results are inaccessible and have never been brought together. For this reason, we have tried to give a unified ac count of the subject and complete proofs of many results. To show what results one might expect, the first chapter deals with the theory of circle diffeomorphisms. The remainder of the book is an attempt to develop the analogous theory in the non-invertible case, despite the intrinsic additional difficulties. In this way, we have tried to show that there is a unified theory in one-dimensional dynamics. By reading one or more of the chapters, the reader can quickly reach the frontier of research. Let us quickly summarize the book. The first chapter deals with circle diffeomorphisms and contains a complete proof of the theorem on the smooth linearizability of circle diffeomorphisms due to M. Herman, J.-C. Yoccoz and others. Chapter II treats the kneading theory of Milnor and Thurstonj also included are an exposition on Hofbauer's tower construction and a result on fuB multimodal families (this last result solves a question posed by J. Milnor).

Table of contents (8 chapters)

  • Introduction

    Melo, Welington (et al.)

    Pages 1-13

  • Circle Diffeomorphisms

    Melo, Welington (et al.)

    Pages 14-80

  • The Combinatorics of One-Dimensional Endomorphisms

    Melo, Welington (et al.)

    Pages 81-200

  • Structural Stability and Hyperbolicity

    Melo, Welington (et al.)

    Pages 201-266

  • The Structure of Smooth Maps

    Melo, Welington (et al.)

    Pages 267-326

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-3-642-78043-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $129.00
price for USA
  • ISBN 978-3-642-78045-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
One-Dimensional Dynamics
Authors
Series Title
Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Series Volume
25
Copyright
1993
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-78043-1
DOI
10.1007/978-3-642-78043-1
Softcover ISBN
978-3-642-78045-5
Series ISSN
0071-1136
Edition Number
1
Number of Pages
XIV, 606
Topics