Dynamical Aspects of Teichmüller Theory

Description

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 number theory. Front Matter ....Pages i-xiv Introduction (Carlos Matheus Silva Santos)....Pages 1-18 Proof of the Eskin-Kontsevich-Zorich Regularity Conjecture (Carlos Matheus Silva Santos)....Pages 19-46 Arithmetic Teichmüller Curves with Complementary Series (Carlos Matheus Silva Santos)....Pages 47-61 Some Finiteness Results for Algebraically Primitive Teichmüller Curves (Carlos Matheus Silva Santos)....Pages 63-78 Simplicity of Lyapunov Exponents of Arithmetic Teichmüller Curves (Carlos Matheus Silva Santos)....Pages 79-104 An Example of Quaternionic Kontsevich-Zorich Monodromy Group (Carlos Matheus Silva Santos)....Pages 105-115 Back Matter ....Pages 117-122