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TMF, 2003, Volume 134, Number 2, Pages 191–206 (Mi tmf150)  

This article is cited in 3 scientific papers (total in 3 papers)

Thermodynamic Formalism and Singular Invariant Measures for Critical Circle Maps

A. A. Dzhalilov

A. Navoi Samarkand State University

Abstract: As is well known, the renormalization group transformation in the space of analytic circle homeomorphisms with one cubic critical point and rotation number equal to the “golden section” has a single fixed point $T_0$. We construct the thermodynamic formalism for the critical map $T_0$ and use it to calculate the Hцlder indices for the singular invariant measure of $T_0$.

Keywords: circle homeomorphism, critical point, thermodynamic formalism, Hölder index

DOI: https://doi.org/10.4213/tmf150

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English version:
Theoretical and Mathematical Physics, 2003, 134:2, 166–180

Bibliographic databases:

Received: 15.01.2002

Citation: A. A. Dzhalilov, “Thermodynamic Formalism and Singular Invariant Measures for Critical Circle Maps”, TMF, 134:2 (2003), 191–206; Theoret. and Math. Phys., 134:2 (2003), 166–180

Citation in format AMSBIB
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\paper Thermodynamic Formalism and Singular Invariant Measures for Critical Circle Maps
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\transl
\jour Theoret. and Math. Phys.
\yr 2003
\vol 134
\issue 2
\pages 166--180
\crossref{https://doi.org/10.1023/A:1022271903129}
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    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:
    1. A. A. Dzhalilov, Kh. K. Karshiboev, “Limit theorems for entrance times of maps of the circle with one break point”, Russian Math. Surveys, 59:1 (2004), 187–188  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. A. A. Dzhalilov, “Limiting Laws for Entrance Times of Critical Mappings of a Circle”, Theoret. and Math. Phys., 138:2 (2004), 190–207  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    3. Poshokhodjaeva G., “Critical Circle Maps and Thermodynamic Formalism”, 37Th International Conference on Quantum Probability and Related Topics (Qp37), Journal of Physics Conference Series, 819, eds. Accardi L., Mukhamedov F., Hee P., IOP Publishing Ltd, 2017, UNSP 012014  crossref  mathscinet  isi  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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