One-Dimensional Dynamics

1. Front Matter

   Pages i-xiii

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2. Introduction

   • Welington de Melo, Sebastian van Strien

   Pages 1-13

3. Circle Diffeomorphisms

   • Welington de Melo, Sebastian van Strien

   Pages 14-80

4. The Combinatorics of One-Dimensional Endomorphisms

   • Welington de Melo, Sebastian van Strien

   Pages 81-200

5. Structural Stability and Hyperbolicity

   • Welington de Melo, Sebastian van Strien

   Pages 201-266

6. The Structure of Smooth Maps

   • Welington de Melo, Sebastian van Strien

   Pages 267-326

7. Ergodic Properties and Invariant Measures

   • Welington de Melo, Sebastian van Strien

   Pages 327-436

8. Renormalization

   • Welington de Melo, Sebastian van Strien

   Pages 437-554

9. Appendix

   • Welington de Melo, Sebastian van Strien

   Pages 555-581

10. Back Matter

    Pages 582-605

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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).

• 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

• Instituto de Matemātica Pura e Applicada, Brazil

  Welington Melo

• Mathematics Department, University of Amsterdam, Amsterdam, The Netherlands

  Sebastian Strien