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Regular and Chaotic Dynamics, 2005, Volume 10, Issue 1, Pages 33–38
DOI: https://doi.org/10.1070/RD2005v010n01ABEH000298 (Mi rcd694) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Generalized dimensions of the golden-mean quasiperiodic orbit from renormalization-group functional equation

S. P. Kuznetsovab

a Saratov Division of Institute, of Radio-Engineering and Electronics, Russian Academy of Sciences, Zelenaya 38, Saratov, 410019, Russia
b Max-Planck-Institut für Physik Komplexer Systeme Nöthnitzer Straße 38, 01187 Dresden, Germany
Citations (2)
DOI: https://doi.org/10.1070/RD2005v010n01ABEH000298
Abstract: A method is suggested for computation of the generalized dimensions for a fractal attractor associated with the quasiperiodic transition to chaos at the golden-mean rotation number. The approach is based on an eigenvalue problem formulated in terms of functional equations with coeficients expressed via the universal fixed-point function of Feigenbaum–Kadanoff–Shenker. The accuracy of the results is determined only by precision of representation of the universal function.
Keywords: circle map, golden mean, renormalization, dimension, generalized dimensions.
Received: 24.02.2005
Accepted: 10.03.2005
Bibliographic databases:
Document Type: Article
MSC: 37C05, 37F25, 37C45, 37C55, 28A80
Language: English
Citation: S. P. Kuznetsov, “Generalized dimensions of the golden-mean quasiperiodic orbit from renormalization-group functional equation”, Regul. Chaotic Dyn., 10:1 (2005), 33–38
Citation in format AMSBIB
\Bibitem{Kuz05}
\by S. P. Kuznetsov
\paper Generalized dimensions of the golden-mean quasiperiodic orbit from renormalization-group functional equation
\jour Regul. Chaotic Dyn.
\yr 2005
\vol 10
\issue 1
\pages 33--38
\mathnet{http://mi.mathnet.ru/rcd694}
\crossref{https://doi.org/10.1070/RD2005v010n01ABEH000298}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2136828}
\zmath{https://zbmath.org/?q=an:1076.37028}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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