Geodesic
Thermodynamic Formalism and Singular Invariant Measures for Critical Circle Maps
Teoretičeskaâ i matematičeskaâ fizika, Tome 134 (2003) no. 2, pp. 191-206

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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. 
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     author = {A. A. Dzhalilov},
     title = {Thermodynamic {Formalism} and {Singular} {Invariant} {Measures} for {Critical} {Circle} {Maps}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {191--206},
     publisher = {mathdoc},
     volume = {134},
     number = {2},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2003_134_2_a3/}
}
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A. A. Dzhalilov. Thermodynamic Formalism and Singular Invariant Measures for Critical Circle Maps. Teoretičeskaâ i matematičeskaâ fizika, Tome 134 (2003) no. 2, pp. 191-206. http://geodesic.mathdoc.fr/item/TMF_2003_134_2_a3/