Critical circle maps and thermodynamic formalism

Let Xk be 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 Xk has a unique fixed point T0. In this paper, we study the properties of orbits of a critical point and build a potential for T0.

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