|
This article is cited in 12 scientific papers (total in 12 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
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 $\mathbb{Q}$
DOI:
https://doi.org/10.4213/faa105
 Full text:
PDF file (229 kB)
References:
PDF file
HTML file
English version:
Functional Analysis and Its Applications, 2004, 38:2, 102–110
Bibliographic databases:
   
UDC:
511.9
Received: 03.02.2003
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://www.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{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000224148100003}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-3142743384}
Linking options:
http://mi.mathnet.ru/eng/faa105https://doi.org/10.4213/faa105 http://mi.mathnet.ru/eng/faa/v38/i2/p28
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
English articles
This publication is cited in the following articles:
-
O. N. Karpenkov, “Classification of three-dimensional multistorey completely empty convex marked pyramids”, Russian Math. Surveys, 60:1 (2005), 165–166
   -
Karpenkov O., “Three examples of three-dimensional continued fractions in the sense of Klein”, C. R. Math. Acad. Sci. Paris, 343:1 (2006), 5–7
-
O. N. Karpenkov, “On an Invariant Möbius Measure and the Gauss–Kuzmin Face Distribution”, Proc. Steklov Inst. Math., 258 (2007), 74–86
-
Karpenkov O.N., “Completely empty pyramids on integer lattices and two-dimensional faces of multidimensional continued fractions”, Monatsh. Math., 152:3 (2007), 217–249
-
Karpenkov O., “Elementary notions of lattice trigonometry”, Math. Scand., 102:2 (2008), 161–205
-
Karpenkov O.N., “Constructing multidimensional periodic continued fractions in the sense of Klein”, Math. Comp., 78:267 (2009), 1687–1711
-
O. N. Karpenkov, “Determination of Periods of Geometric Continued Fractions for Two-Dimensional Algebraic Hyperbolic Operators”, Math. Notes, 88:1 (2010), 28–38
-
Karpenkov O.N., Vershik A.M., “Rational approximation of maximal commutative subgroups of GL(n, R)”, J Fixed Point Theory Appl, 7:1 (2010), 241–263
-
Karpenkov O., “Continued fractions and the second Kepler law”, Manuscripta Math, 134:1–2 (2011), 157–169
-
Karpenkov O., “Multidimensional Gauss Reduction Theory for Conjugacy Classes of Sl(N, Z)”, J. Theor. Nr. Bordx., 25:1 (2013), 99–109
-
A. A. Illarionov, “Some properties of three-dimensional Klein polyhedra”, Sb. Math., 206:4 (2015), 510–539
-
A. A. Lodkin, “Parus Kleina i diofantovy priblizheniya vektora”, Teoriya predstavlenii, dinamicheskie sistemy, kombinatornye i algoritmicheskie metody. XXX, Zap. nauchn. sem. POMI, 481, POMI, SPb., 2019, 63–73
|
| Number of views: |
| This page: | 473 | | Full text: | 160 | | References: | 67 |
|
Terms of Use