Continued Fraction Expansions of Matrix Eigenvectors

2008/10/11 by Maria Pavlovskaia, Pavlovskaia, Maria
Computer Science · Mathematics · #11A55 #FOS: Mathematics #Mathematical Dynamics and Fractals #Matrix Theory and Algorithms #Number Theory (math.NT) #math.NT #msc:11A55 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.0810.2054

10 pages, 7 figures

arxiv created 2008/10/11 · openalex publication_date 2008/10/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We examine various properties of the continued fraction expansions of matrix eigenvector slopes of matrices from the SL(2, Z) group. We calculate the average period length, maximum period length, average period sum, maximum period sum and the distributions of 1s 2s and 3s in the periods versus the radius of the Ball within which the matrices are located. We also prove that the periods of continued fraction expansions from the real irrational roots of x2 + px + q = 0 are always palindromes.

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