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.
By:
Yiheng Dong, Marco Martens, Liviana Palmisano Imprint: Springer International Publishing AG Country of Publication: Switzerland Volume: 30 Dimensions:
Height: 235mm,
Width: 155mm,
ISBN:9783031948817 ISBN 10: 3031948815 Series:Lecture Notes of the Unione Matematica Italiana Pages: 181 Publication Date:01 September 2025 Audience:
Professional and scholarly
,
Undergraduate
Format:Paperback Publisher's Status: Active
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.