| Abstrakt: |
Let T ∈ C 2 + ε (S 1 \ { x b }) , ε > 0 , be a circle homeomorphism with one break point xb, at which T'(x) has a discontinuity of the first kind and both one-sided derivatives at the point xb are strictly positive. Assume that the rotation number ρT is irrational with continued fraction decomposition ρ T = [ m 1 , m 2 , ... , m l , m l + 1 , ... ] , m s = k , s > l > 0. We construct a thermodynamic formalism for homeomorphisms T b ∈ C 2 + ε (S 1 \ { x b }) , ε> 0, with break point xb and rotation number ω = − k + k 2 + 4 2 , k ≥ 1. Using the thermodynamic formalism, we investigate the exponents of singularity of unique probability invariant measure µT of homeomorphism T. [ABSTRACT FROM AUTHOR] |
