New sequences of non-free rational points

2021/01/04 by Smilga, Ilia · 2 citations
#11C20 (Primary) 20E05 #11J70 #30F35 (Secondary) #FOS: Mathematics #Group Theory (math.GR) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2101.00872

Abstract

We exhibit some new infinite families of rational values of τ, some of them squares of rationals, for which the group or even the semigroup generated by the matrices ( \beginsmallmatrix 1 & 1 0 & 1 \endsmallmatrix ) and ( \beginsmallmatrix 1 & 0 τ& 1 \endsmallmatrix ) is not free.

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• On non-freeness of groups generated by two parabolic matrices with rational parameters: limit points and the orbit test
• Easy estimates of Lyapunov exponents for random products of matrices

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