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Matematicheskie Trudy, 2007, Volume 10, Number 1, Pages 97–131 (Mi mt30)  
This article is cited in 10 scientific papers (total in 10 papers)

Continued Fractions, the Group $\mathrm{GL}(2,\mathbb Z)$, and Pisot Numbers

V. N. Berestovskiia, Yu. G. Nikonorovb

a Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Science
b Rubtsovsk Industrial Intitute, Branch of Altai State Technical University
Full-text PDF (365 kB) Citations (10) English version article
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Abstract: The properties of continued fractions, generalized golden sections, and generalized Fibonacci and Lucas numbers are proved on the ground of the properties of subsemigroups of the group of invertible integer matrices. Some properties of special recurrent sequences are studied. A new proof of the Pisot-Vijayaraghavan theorem is given. Some connections between continued fractions and Pisot numbers are considered. Some unsolved problems are stated.
Key words: continued fractions, Pisot numbers, recurrent sequences, generalized Fibonacci and Lucas numbers.
Received: 26.01.2006
English version:
Siberian Advances in Mathematics, 2007, Volume 17, Issue 4, Pages 268–290
DOI: https://doi.org/10.3103/S1055134407040025
Bibliographic databases:
UDC: 511.26
Language: Russian
Citation: V. N. Berestovskii, Yu. G. Nikonorov, “Continued Fractions, the Group $\mathrm{GL}(2,\mathbb Z)$, and Pisot Numbers”, Mat. Tr., 10:1 (2007), 97–131; Siberian Adv. Math., 17:4 (2007), 268–290
Citation in format AMSBIB
\Bibitem{BerNik07}
\by V.~N.~Berestovskii, Yu.~G.~Nikonorov
\paper Continued Fractions, the Group $\mathrm{GL}(2,\mathbb Z)$, and Pisot Numbers
\jour Mat. Tr.
\yr 2007
\vol 10
\issue 1
\pages 97--131
\mathnet{http://mi.mathnet.ru/mt30}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=2485367}
\elib{https://elibrary.ru/item.asp?id=9483455}
\transl
\jour Siberian Adv. Math.
\yr 2007
\vol 17
\issue 4
\pages 268--290
\crossref{https://doi.org/10.3103/S1055134407040025}
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    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические труды Siberian Advances in Mathematics
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