This article is cited in 10 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.

Received: 15.01.2002

DOI: 10.4213/tmf150

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

Bibliographic databases:

• 
• 
•