Exponential growth of product of matrices in SL(2, ℝ)

Bassam Fayad; Raphal Krikorian

doi:10.1088/0951-7715/21/2/007

Exponential growth of product of matrices in SL(2, ℝ)

Bassam Fayad
, Raphal Krikorian

University Paris 13
Sorbonne Université

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper we investigate the exponential growth of products of two matrices . We prove, assuming A is a fixed hyperbolic matrix, that for Lebesgue almost every B, products of length n involving less than n^α, 0 ≤ α < 1/2 matrices B are uniformly bounded from below by γⁿ for some γ > 1.

Original language	English
Pages (from-to)	319-323
Number of pages	5
Journal	Nonlinearity
Volume	21
Issue number	2
DOIs	https://doi.org/10.1088/0951-7715/21/2/007
Publication status	Published - 1 Feb 2008

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abstract = "In this paper we investigate the exponential growth of products of two matrices . We prove, assuming A is a fixed hyperbolic matrix, that for Lebesgue almost every B, products of length n involving less than nα, 0 ≤ α < 1/2 matrices B are uniformly bounded from below by γn for some γ > 1.",

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N2 - In this paper we investigate the exponential growth of products of two matrices . We prove, assuming A is a fixed hyperbolic matrix, that for Lebesgue almost every B, products of length n involving less than nα, 0 ≤ α < 1/2 matrices B are uniformly bounded from below by γn for some γ > 1.

AB - In this paper we investigate the exponential growth of products of two matrices . We prove, assuming A is a fixed hyperbolic matrix, that for Lebesgue almost every B, products of length n involving less than nα, 0 ≤ α < 1/2 matrices B are uniformly bounded from below by γn for some γ > 1.

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JO - Nonlinearity

JF - Nonlinearity

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Exponential growth of product of matrices in SL(2, ℝ)

Abstract

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