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Funktsional'nyi Analiz i ego Prilozheniya, 2004, Volume 38, Issue 2, Pages 28–37
DOI: https://doi.org/10.4213/faa105 (Mi faa105) 		 
This article is cited in 17 scientific papers (total in 17 papers)

On Tori Triangulations Associated with Two-Dimensional Continued Fractions of Cubic Irrationalities

O. N. Karpenkov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (229 kB) Citations (17)
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DOI: https://doi.org/10.4213/faa105
Abstract: 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.
Keywords: multidimensional continued fractions, convex hulls, integer operators, cubic extensions of $\mathbb{Q}$.
Received: 03.02.2003
English version:
Functional Analysis and Its Applications, 2004, Volume 38, Issue 2, Pages 102–110
DOI: https://doi.org/10.1023/B:FAIA.0000034040.08573.22
Bibliographic databases:
Document Type: Article
UDC: 511.9
Language: Russian
Citation: O. N. Karpenkov, “On Tori Triangulations Associated with Two-Dimensional Continued Fractions of Cubic Irrationalities”, Funktsional. Anal. i Prilozhen., 38:2 (2004), 28–37; Funct. Anal. Appl., 38:2 (2004), 102–110
Citation in format AMSBIB
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    • This publication is cited in the following 17 articles:
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    		Функциональный анализ и его приложения Functional Analysis and Its Applications
     
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