Open AccessUniform exponential growth for some <em>SL(2, R)</em> matrix products
Author(s) -
Artur Avila,
Thomas Roblin
Publication year - 2009
Publication title -
journal of modern dynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.668
H-Index - 25
eISSN - 1930-532X
pISSN - 1930-5311
DOI - 10.3934/jmd.2009.3.549
Subject(s) - matrix (chemical analysis) , exponential growth , combinatorics , product (mathematics) , mathematics , exponential function , mathematical analysis , geometry , chemistry , chromatography
Given a hyperbolic matrix $H\in SL(2,\R)$, we prove that for almost every $R\in SL(2,\R)$, any product of length $n$ of $H$ and $R$ grows exponentially fast with $n$ provided the matrix $R$ occurs less than $o(\frac{n}{\log n\log\log n})$ times.
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