Funktsional'nyi Analiz i ego Prilozheniya
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Funktsional. Anal. i Prilozhen.:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

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)
References:
PDF
HTML
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
\Bibitem{Kar04}
\by O.~N.~Karpenkov
\paper On Tori Triangulations Associated with Two-Dimensional Continued Fractions of Cubic Irrationalities
\jour Funktsional. Anal. i Prilozhen.
\yr 2004
\vol 38
\issue 2
\pages 28--37
\mathnet{http://mi.mathnet.ru/faa105}
\crossref{https://doi.org/10.4213/faa105}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2086625}
\zmath{https://zbmath.org/?q=an:1125.11042}
\transl
\jour Funct. Anal. Appl.
\yr 2004
\vol 38
\issue 2
\pages 102--110
\crossref{https://doi.org/10.1023/B:FAIA.0000034040.08573.22}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000224148100003}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-3142743384}
Linking options:
  • https://www.mathnet.ru/eng/faa105
  • https://doi.org/10.4213/faa105
  • https://www.mathnet.ru/eng/faa/v38/i2/p28
    • This publication is cited in the following 17 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
    Statistics & downloads:
    Abstract page:697
    Full-text PDF :242
    References:99
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024