Exponential decay of correlations for the Rauzy-Veech-Zorich induction map

Decay of Correlations for the Rauzy-veech-zorich Induction Map on the Space of Interval Exchange Transformations and the Central Limit Theorem for the Teichmüller Flow on the Moduli Space of Abelian Differentials

The aim of this paper is to prove a stretched-exponential bound for the decay of correlations for the Rauzy-Veech-Zorich induction map on the space of interval exchange transformations (Theorem 4). A corollary is the Central Limit Theorem for the Teichmüller flow on the moduli space of abelian differentials with prescribed singularities (Theorem 10). The proof of Theorem 4 proceeds by the metho...

Decay of Correlations for the Rauzy–Veech–Zorich Induction Map on the Space of Interval Exchange Transformations

Decay of Correlations for the Rauzy–Veech–Zorich Induction Map on the Space of Exchanges of Four Intervals

Decoding Rauzy Induction: Bufetov’s Question

Answering a question posed by Alexander Bufetov, it is proved that if a pair of (i.d.o.c.) interval exchanges on [0, 1) have identical sequences of visitation matrices with respect to Rauzy induction, then the exchanges are homeomorphically conjugate and, in particular, are governed by the same permutation. 2000 Math. Subj. Class. 37E05, 37B10.

Introduction to Teichmüller Theory and Its Applications to Dynamics of Interval Exchange Transformations, Flows on Surfaces and Billiards

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 Teichmüller and moduli space of translation surfaces, the Teich...