Karpenkov, O. N. On tori triangulations associated with two-dimensional continued fractions of cubic irrationalities. (English. Russian original) Zbl 1125.11042 Funct. Anal. Appl. 38, No. 2, 102-110 (2004); translation from Funkts. Anal. Prilozh. 38, No. 2, 28-37 (2004). Summary: The notion of equivalence of multidimensional continued fractions is introduced. We consider some properties and state some conjectures related to the structure of the family of equivalence classes of two-dimensional periodic continued fractions. Our approach to the study of the family of equivalence classes of two-dimensional periodic continued fractions leads to revealing special subfamilies of continued fractions for which the triangulations of the torus (i.e., the combinatorics of their fundamental domains) are subjected to clear rules. Some of these subfamilies are studied in detail; the way to construct other similar subfamilies is indicated. Cited in 10 Documents MSC: 11J70 Continued fractions and generalizations 11A55 Continued fractions 11H46 Products of linear forms Keywords:multidimensional continued fractions; convex hulls; integer operators; cubic extensions of PDFBibTeX XMLCite \textit{O. N. Karpenkov}, Funct. Anal. Appl. 38, No. 2, 102--110 (2004; Zbl 1125.11042); translation from Funkts. Anal. Prilozh. 38, No. 2, 28--37 (2004) Full Text: DOI arXiv