One-Dimensional Dynamics
From Poincaré to renormalization
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Beschreibung
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.
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.
Presents one of the deepest theories in dynamics No prerequisites are needed Here is an introduction to dynamics!
Autor*in
Yiheng Dong
Themen in »One-Dimensional Dynamics«
Renormalization Circle maps Rigidity Thurston method Topological classes Hyperbolicity