Farey graph and rational fixed points of the extended modular group
نویسندگان
چکیده
Fixed points of matrices have many applications in various areas science and mathematics. Extended modular group ¯¯¯¯ΓΓ¯ is the 2×22×2 with integer entries determinant ±1±1. There are strong connections between extended group, continued fractions Farey graph. graph a vertex set ^Q=Q∪{∞}Q^=Q∪{∞}. In this study, we consider elements that fix rationals. For given rational number, use its neighbours to obtain matrix representation element $\overline{\Gamma}$ fixes rational. Then express such as words terms generators using relations fractions. Finally give new block reduced form these which all blocks Fibonacci numbers entries.
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ژورنال
عنوان ژورنال: Communications Faculty of Sciences University of Ankara. Series A1: mathematics and statistics
سال: 2022
ISSN: ['1303-5991']
DOI: https://doi.org/10.31801/cfsuasmas.1089480