Home Newsletter
News Books
Welcome to FreeScience.info Language/Lingua

Books 3054
· Book News
· Most clicked
· Least clicked

Search for a Book
HELP US TO HELP YOU
Add a new Book

Introduction to Teichmüller theory and its applications to dynamics of interval exchange transformations, flows on surfaces and

book
Language:
Author: Giovanni Forni, Carlos Matheus
Url: http://arxiv.org/abs/1311.2758
Format: Ps, Pdf
Year: 2013
Category: Dynamic systems
Pages: 157
Clicks: 843

Description
This text is an expanded version of the lecture notes of a minicourse (with the same title of this text) delivered by the authors in the Bedlewo school "Modern Dynamics and its Interaction with Analysis, Geometry and Number Theory" (from 4 to 16 July, 2011). In the first part of this text, i.e., from Sections 1 to 5, we discuss the Teichm\"uller and moduli space of translation surfaces, the Teichm\"uller flow and the SL(2,R)-action on these moduli spaces and the Kontsevich-Zorich cocycle over the Teichm\"uller geodesic flow. We sketch two applications of the ergodic properties of the Teichm\"uller flow and Kontsevich-Zorich cocycle, with respect to Masur-Veech measures, to the unique ergodicity, deviation of ergodic averages and weak mixing properties of typical interval exchange transformations and translation flows. These applications are based on the fundamental fact that the Teichm\"uller flow and the Kontsevich-Zorich cocycle work as \emph{renormalization dynamics} for interval exchange transformations and translation flows. In the second part, i.e., from Sections 6 to 9, we start by pointing out that it is interesting to study the ergodic properties of the Kontsevich-Zorich cocycle with respect to invariant measures other than the Masur-Veech ones, in view of potential applications to the investigation of billiards in rational polygons (for instance). We then study some examples of measures for which the ergodic properties of the Kontsevich-Zorich cocycle are very different from the case of Masur-Veech measures. Finally, we end these notes by constructing some examples of closed SL(2,R)-orbits such that the restriction of the Teichm\"uller flow to them has arbitrary small rate of exponential mixing, or, equivalently, the naturally associated unitary SL(2,R)-representations have arbitrarily small spectral gap (and in particular it has complementary series).

Similar Books
Introduzione ai sistemi dinamici
Sistemi dinamici
Kinetic Theory of Dynamical Systems
Perturbation theory of dynamical systems
Sistemi dinamici
Introduzione ai sistemi dinamici
Perturbation theory of dynamical systems
Geometrical theory of dynamical systems
An Introduction To Small Divisors
Dynamical Systems
Dynamical Systems
These notes study the dynamics of iterated holomorphic mappings
Lectures on Mechanics, Dynamics, and Symmetry
Dynamical systems
Ordinary Differential Equations and Dynamical Systems
Dynamical Systems and Fractals Lecture Notes
Nonlinear Dynamics
From Deterministic Chaos to Deterministic Diffusion
The Lyapunov Characteristic Exponents and their computation Authors:
Monotone Dynamical Systems
Ergodic optimization, zero temperature limits and the max-plus algebra
Around the boundary of complex dynamics

Home |  Authors | About | Contact Us |  Email 
 Copyright © 2002-2013 FreeScience.info. 

Best viewed with Mozilla 1.X 1024x768
free scientific books