On the Size of the Resonant Set for the Products of 2x2 Matrices

Details On the Size of the Resonant Set for the Products of 2x2 Matrices On the Size of the Resonant Set for the Products of 2x2 Matrices

2011-06-15

arxiv.org/abs/1106.2903v1

Mathematics

Dynamical Systems

10 pages, 7 figures, acknowledgements to Professors Serguei Denissov and Alexander Kiselev; Involve - A Journal of Mathematics

Scientific paper

For {\theta} \in [0, 2{\pi}), consider the rotation matrix R? and h = ({\lambda}, 0; 0, 0), {\lambda} > 1. Let W_n({\theta}) denote the product of m R?'s and n h's with the condition m \leq [\epsilon\astn], (0 < \epsilon < 1). We analyze the measure of the set of {\theta} for which ||W_n({\theta})|| \geq {\lambda}?^(n*{\delta}), (0 < {\delta} < 1). This can be regarded as a model problem for the so-called Bochi-Fayad conjecture.

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