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, 2010, Volume 44, Issue 2, Pages 3–13
DOI: https://doi.org/10.4213/faa2990 (Mi faa2990) 		 
This article is cited in 2 scientific papers (total in 2 papers)

The Erdős–Vershik problem for the golden ratio

Z. I. Bezhaevaa, V. I. Oseledetsb

a Moscow State Institute of Electronics and Mathematics
b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (192 kB) Citations (2)
References:
PDF
HTML
DOI: https://doi.org/10.4213/faa2990
Abstract: Properties of the Erdős measure and the invariant Erdős measure for the golden ratio and all values of the Bernoulli parameter are studied. It is proved that a shift on the two-sided Fibonacci compact set with invariant Erdős measure is isomorphic to the integral automorphism for a Bernoulli shift with countable alphabet. An effective algorithm for calculating the entropy of an invariant Erdős measure is proposed. It is shown that, for certain values of the Bernoulli parameter, this algorithm gives the Hausdorff dimension of an Erdős measure to 15 decimal places.
Keywords: hidden Markov chain, Erdős measure, invariant Erdős measure, golden shift, integral automorphism, entropy, Hausdorff dimension of a measure.
Received: 22.08.2008
English version:
Functional Analysis and Its Applications, 2010, Volume 44, Issue 2, Pages 83–91
DOI: https://doi.org/10.1007/s10688-010-0012-3
Bibliographic databases:
Document Type: Article
UDC: 517.987.5+519.21
Language: Russian
Citation: Z. I. Bezhaeva, V. I. Oseledets, “The Erdős–Vershik problem for the golden ratio”, Funktsional. Anal. i Prilozhen., 44:2 (2010), 3–13; Funct. Anal. Appl., 44:2 (2010), 83–91
Citation in format AMSBIB
\Bibitem{BezOse10}
\by Z.~I.~Bezhaeva, V.~I.~Oseledets
\paper The Erd\H{o}s--Vershik problem for the golden ratio
\jour Funktsional. Anal. i Prilozhen.
\yr 2010
\vol 44
\issue 2
\pages 3--13
\mathnet{http://mi.mathnet.ru/faa2990}
\crossref{https://doi.org/10.4213/faa2990}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2681954}
\zmath{https://zbmath.org/?q=an:1231.28015}
\transl
\jour Funct. Anal. Appl.
\yr 2010
\vol 44
\issue 2
\pages 83--91
\crossref{https://doi.org/10.1007/s10688-010-0012-3}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000279129200002}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77954159544}
Linking options:
  • https://www.mathnet.ru/eng/faa2990
  • https://doi.org/10.4213/faa2990
  • https://www.mathnet.ru/eng/faa/v44/i2/p3
    • This publication is cited in the following 2 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
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024