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One-Dimensional Dynamics

  • Welington de Melo
  • Sebastian van Strien

Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE3, volume 25)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Welington de Melo, Sebastian van Strien
    Pages 1-13
  3. Welington de Melo, Sebastian van Strien
    Pages 14-80
  4. Welington de Melo, Sebastian van Strien
    Pages 81-200
  5. Welington de Melo, Sebastian van Strien
    Pages 201-266
  6. Welington de Melo, Sebastian van Strien
    Pages 267-326
  7. Welington de Melo, Sebastian van Strien
    Pages 327-436
  8. Welington de Melo, Sebastian van Strien
    Pages 437-554
  9. Welington de Melo, Sebastian van Strien
    Pages 555-581
  10. Back Matter
    Pages 582-605

About this book

Introduction

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).

Keywords

Dynamical Systems Dynamische Systeme Eindimensionale dynamische Systeme Interval dynamics Intervalldynamik Iterationen im Intervall Iterations on the interval One-dimensional dynamics Power Universality Universalität ergodic theory ergodicity functional analysis measure theory

Authors and affiliations

  • Welington de Melo
    • 1
  • Sebastian van Strien
    • 2
  1. 1.Instituto de Matemātica Pura e ApplicadaBrazil
  2. 2.Mathematics DepartmentUniversity of AmsterdamAmsterdamThe Netherlands

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-78043-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 1993
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-78045-5
  • Online ISBN 978-3-642-78043-1
  • Series Print ISSN 0071-1136
  • Buy this book on publisher's site
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