Dynamical Aspects of Teichmüller Theory

This book is a remarkable contribution to the literature on dynamical systems and geometry. It consists of a selection of work in current research on Teichmüller dynamics, a field that has continued to develop rapidly in the past decades. After a comprehensive introduction, the author investigates the dynamics of the Teichmüller flow, presenting several self-contained chapters, each addressing a different aspect on the subject. The author includes innovative expositions, all the while solving open problems, constructing examples, and supplementing with illustrations. This book is a rare find in the field with its guidance and support for readers through the complex content of moduli spaces and Teichmüller Theory.

The author is an internationally recognized expert in dynamical systems with a talent to explain topics that is rarely found in the field. He has created a text that would benefit specialists in, not only dynamical systems and geometry, but also Lie theory and numbertheory.

The book gives easy access to recent research topics in Teichmüller dynamics; the results described were obtained after 2012 The book provides streamlined and partly new versions of the proofs of these recent research results After the introduction, each chapter can be read independently from one another, dealing with different aspects of Teichmüller dynamics. They are self-contained moduli of the background content introduced in the first chapter

Autorentext
Carlos Matheus Silva Santos is a Brazilian mathematician who is an expert in the field of dynamical systems. He currently works at the Centre national de la recherche scientifique (CNRS), while teaching at both École Polytechnique and Université Paris 13. Additionally, he has organized various conferences in Paris and Rio de Janiero on the topic of dynamical systems.

Inhalt
Introduction.- Proof of the Eskin-Kontsevich-Zorich Regularity Conjecture.- Arithmetic Teichmüller Curves with Complementary Series.- Some Finiteness Results for Algebraically Primitive Teichmüller Curves.- Simplicity of Lyapunov Exponents of Arithmetic Teichmüller Curves.- An Example of Quaternionic Kontsevich-Zorich Monodromy Group.