One-Dimensional Dynamics: From Poincaré to renormalization
Author:   Yiheng Dong ,  Marco Martens ,  Liviana Palmisano
Publisher:   Springer International Publishing AG
Volume:   30
ISBN:  

9783031948817


Pages:   200
Publication Date:   20 July 2025
Format:   Paperback
Availability:   Not yet available   Availability explained
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One-Dimensional Dynamics: From Poincaré to renormalization


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Overview

The aim of the book is to give an introduction to the main concepts in modern dynamics. The Herman Theorem on rigidity of circle diffeomoprhisms is used to achieve this goal. Indeed, we reprove this sophisticated theorem with modern techniques involving renormalization and, in the meantime, discuss most of the important concepts used in dynamics. The one-dimensional context of the Herman Theorem reduces the technical difficulties and allows to present tools and theories to students with modest background. The book can definitely be used on Master's level.

Full Product Details

Author:   Yiheng Dong ,  Marco Martens ,  Liviana Palmisano
Publisher:   Springer International Publishing AG
Imprint:   Springer International Publishing AG
Volume:   30
ISBN:  

9783031948817


ISBN 10:   3031948815
Pages:   200
Publication Date:   20 July 2025
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Forthcoming
Availability:   Not yet available   Availability explained
This item is yet to be released. You can pre-order this item and we will dispatch it to you upon its release.

Table of Contents

Chapter 1. Introduction.- Chapter 2. Topology of Circle Homeomorphisms.- Chapter 3. Topology of Circle Diffeomorphisms.- Chapter 4. Renormalization.- Chapter 5. The Three Ingredients for Convergence of Renormalization.- Chapter 6. The Collaboration of the Three Ingredients.- Chapter 7. Exponential Convergence.- Chapter 8. Geometry of Circle Diffeomorphisms.- Chapter 9. Non-Rigidity.- Chapter 10. The Renormalization Horseshoe.

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