On tori triangulations associated with two-dimensional continued fractions of cubic irrationalities

Details On tori triangulations associated with two-dimensional continued fractions of cubic irrationalities On tori triangulations associated with two-dimensional continued fractions of cubic irrationalities

2009-11-16

arxiv.org/abs/0911.3025v1

Funktsional. Anal. i Prilozhen. 38 (2004), no. 2, 28--37, 95; translation in Funct. Anal. Appl. 38 (2004), no. 2, 102--110

Mathematics

Number Theory

Scientific paper

10.1023/B:FAIA.0000034040.08573.

We show several properties related to the structure of the family of classes of two-dimensional periodic continued fractions. This approach to the study of the family of classes of nonequivalent two dimexsional periodic continued fractions leads to the visualization of special subfamilies of continued fractions with torus triangulations (i.e. combinatorics of their fundamental domains) that possess explicit regularities.Several cases of such subfamilies are studied in detail; the method to construct other similar subfamilies is given.

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