Critical circle maps and thermodynamic formalism

37th International Conference on Quantum Probability and Related Topics

Poshokhodjaeva, Gulnora^1

Department of Mechanics and Mathematics, Samarkand State University, Samarkand, Uzbekistan^1

关键词: Circle map;    Fixed points;    Renormalization;    Rotation number;    Thermodynamic formalism;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/819/1/012014/pdf
DOI  :  10.1088/1742-6596/819/1/012014

来源: IOP

【 摘 要 】

Let Xkbe the space of analytic, critical circle homeomorphisms with an irrational rotation number ρk= [k, k,..., k,...]. It is shown [S. Ostlund, D. Rand, J. Sethna and E. Siggia, Physica D,8 (1983) 303] that, the renormalization operator defined on Xkhas a unique fixed point T0. In this paper, we study the properties of orbits of a critical point and build a potential for T0.