Summary: Uniformly Hyperbolic Finite-Valued
SL(2, R)-Cocycles
A. Avila, J. Bochi, and J.-C. Yoccoz
August 1, 2008
Abstract
We consider finite families of SL(2, R) matrices whose products display
uniform exponential growth. These form open subsets of (SL(2, R))N
, and
we study their components, boundary, and complement. We also consider
the more general situation where the allowed products of matrices satisfy
a Markovian rule.
Contents
1 Introduction 2
2 Multicones 5
2.1 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Proof of the "If" Part of Theorem 2.3 . . . . . . . . . . . . . . . . 6
2.3 Proof of the "Only If" Part of Theorem 2.3 . . . . . . . . . . . . . 9
2.4 The Case of Full Shifts . . . . . . . . . . . . . . . . . . . . . . . . 11
3 The Full 2-Shift Case 13
3.1 Statements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Source: Avila, Artur - Instituto Nacional de Matemática Pura e Aplicada (IMPA)

Collections: Mathematics