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000856193 1001_ $$aSantos, Carlos Matheus Silva,$$eauthor.
000856193 24510 $$aDynamical aspects of teichmüller theory :$$bSL(2,R)-action on moduli spaces of flat surfaces /$$cCarlos Matheus Silva Santos.
000856193 264_1 $$aCham :$$bSpringer ;$$a[Amsterdam] :$$bAtlantis Press,$$c[2018]
000856193 264_4 $$c©2018
000856193 300__ $$a1 online resource.
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000856193 4901_ $$aAtlantis series in dynamical systems ;$$vvolume 7
000856193 504__ $$aIncludes bibliographical references and index.
000856193 5050_ $$aIntro; Preface; Acknowledgements; Contents; 1 Introduction; 1.1 Abelian Differentials and Their Moduli Spaces; 1.2 Translation Structures; 1.3 Some Examples of Translation Surfaces; 1.3.1 Abelian Differentials on Complex Torus; 1.3.2 Square-Tiled Surfaces; 1.3.3 Suspensions of Interval Exchange Transformations; 1.3.4 Billiards in Rational Polygons; 1.4 Stratification of Moduli Spaces of Translation Surfaces; 1.5 Period Coordinates; 1.6 Connected Components of Strata; 1.7 GL+(2,mathbbR) Action on mathcalHg; 1.8 SL(2,mathbbR)-Action on mathcalHg.
000856193 5058_ $$a1.9 Teichmüller Flow and Kontsevich-Zorich Cocycle1.10 Teichmüller Curves, Veech Surfaces and Affine Homeomorphisms; 2 Proof of the Eskin-Kontsevich-Zorich Regularity Conjecture; 2.1 Eskin-Kontsevich-Zorich Formula; 2.2 Statement of the Eskin-Kontsevich-Zorich Regularity Conjecture; 2.3 Idea of the Proof of Theorem 9; 2.4 Reduction of Theorem 9 to Propositions 14 and 15; 2.5 Proof of Proposition 14 (Modulo Propositions 16 and 17); 2.6 Proof of Proposition 15 (Modulo Proposition 16); 2.7 Proof of Proposition 16 via Rokhlin's Disintegration Theorem.
000856193 5058_ $$a2.8 Proof of Proposition 17 via Rokhlin's Disintegration Theorem3 Arithmetic Teichmüller Curves with Complementary Series; 3.1 Exponential Mixing of the Teichmüller Flow; 3.2 Teichmüller Curves with Complementary Series; 3.3 Idea of Proof of Theorem 40; 3.4 Quick Review of Representation Theory of SL(2,mathbbR); 3.4.1 Spectrum of Unitary SL(2,mathbbR)-Representations; 3.4.2 Bargmann's Classification; 3.4.3 Hyperbolic Surfaces and Examples of Regular Unitary SL(2,mathbbR)-Representations; 3.4.4 Rates of Mixing and Spectral Gap.
000856193 5058_ $$a5.2 Lyapunov Exponents of Teichmüller Curves and Random Products of Matrices5.3 Galois-Theoretical Criterion for Simplicity of Exponents of Origamis; 5.3.1 Galois-Pinching Matrices; 5.3.2 Twisting with Respect to Galois-Pinching Matrices I: Statements of Results; 5.3.3 Twisting with Respect to Galois-Pinching Matrices II: Proof of Theorem 67; 5.3.4 Two Simplicity Criteria for the Lyapunov Exponents of Origamis; 5.4 A Counterexample to an Informal Conjecture of Forni; 6 An Example of Quaternionic Kontsevich-Zorich Monodromy Group.
000856193 506__ $$aAccess limited to authorized users.
000856193 520__ $$aThis book is a remarkable contribution to the literature on dynamical systems and geometry. It consists of a selection of work in current research on Teichmüller dynamics, a field that has continued to develop rapidly in the past decades. After a comprehensive introduction, the author investigates the dynamics of the Teichmüller flow, presenting several self-contained chapters, each addressing a different aspect on the subject. The author includes innovative expositions, all the while solving open problems, constructing examples, and supplementing with illustrations. This book is a rare find in the field with its guidance and support for readers through the complex content of moduli spaces and Teichmüller Theory. The author is an internationally recognized expert in dynamical systems with a talent to explain topics that is rarely found in the field. He has created a text that would benefit specialists in, not only dynamical systems and geometry, but also Lie theory and number theory.--$$cProvided by publisher.
000856193 588__ $$aOnline resource; title from PDF title page (viewed July 16, 2018).
000856193 650_0 $$aDynamics.
000856193 650_0 $$aTeichmüller spaces.
000856193 650_0 $$aGeometry.
000856193 650_0 $$aModuli theory.
000856193 77608 $$iPrint version:$$aSantos, Carlos Matheus Silva.$$tDynamical aspects of teichmüller theory.$$dCham : Springer ; [Amsterdam] : Atlantis Press, [2018]$$z3319921584$$z9783319921587$$w(OCoLC)1032019769
000856193 830_0 $$aAtlantis series in dynamical systems ;$$vv. 7.
000856193 852__ $$bebk
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