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

Matematicheskie Trudy

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	General information
	Latest issue
	Archive
	Impact factor

	Search papers
	Search references

	RSS
	Latest issue
	Current issues
	Archive issues
	What is RSS

Mat. Tr.:
Year:
Volume:
Issue:
Page:
	Find

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

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. Berestovskii^a, Yu. G. Nikonorov^b

^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)

References:

PDF

HTML

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{http://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}

Linking options:

https://www.mathnet.ru/eng/mt30

https://www.mathnet.ru/eng/mt/v10/i1/p97

This publication is cited in the following 10 articles:

S.L. Gefter, A.L. Piven', “Implicit Linear Nonhomogeneous Difference Equation over ℤ with a Random Right-Hand Side”, Z. mat. fiz. anal. geom., 18:1 (2022), 105
S. L. Gefter, V. V. Martseniuk, A. B. Goncharuk, A. L. Piven', “Analogue of the Cramer Rule for an Implicit Linear Second Order Difference Equation Over the Ring of Integers”, J Math Sci, 244:4 (2020), 601
V. V. MARTSENIUK, Sergey L. Gefter, A. L. Piven', Springer Proceedings in Mathematics & Statistics, 341, Progress on Difference Equations and Discrete Dynamical Systems, 2020, 311
O. Piven, V. Martseniuk, S. Hefter, “INTEGER SOLUTIONS OF A SECOND ORDER IMPLICIT LINEAR DIFFERENCE EQUATION”, BMJ, 6:3-4 (2018), 40
S.L. Gefter, A.B. Goncharuk, A.L. Piven', “Integer solutions for a vector implicit linear difference equation in ZN”, Dopov. Nac. akad. nauk Ukr., 2018, no. 11, 11
N. M. Dobrovolskii, N. N. Dobrovolskii, D. K. Sobolev, V. N. Soboleva, “Klassifikatsiya chisto-veschestvennykh algebraicheskikh irratsionalnostei”, Chebyshevskii sb., 18:2 (2017), 98–128
N. M. Dobrovol'skii, I. N. Balaba, I. Yu. Rebrova, N. N. Dobrovol'skii, “On Lagrange algorithm for reduced algebraic irrationalities”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2016, no. 2, 27–39
Nikolai M. Dobrovol'skii, Nikolai N. Dobrovolsky, Irina N. Balaba, Irina Yu. Rebrova, Dmitrii K. Sobolev, Valentina N. Soboleva, Studies in Systems, Decision and Control, 69, Advances in Dynamical Systems and Control, 2016, 81
N. M. Dobrovol'skii, N. N. Dobrovol'skii, “About minimal polynomial residual fractions for algebraic irrationalities”, Doklady Mathematics (Supplementary issues), 106:2 (2022), 165–180
T. A. Kozlovskaya, “Konkho-spirali na poverkhnosti konusa”, Vestn. NGU. Ser. matem., mekh., inform., 11:2 (2011), 65–76

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Statistics & downloads:
Abstract page:	1102
Full-text PDF :	508
References:	124
First page:	1

Что такое QR-код?

Registration to the website

Logotypes