Singular measures in circle dynamics. (English) Zbl 0792.58025

The authors consider a smooth circle homeomorphism with finitely many critical points of polynomial type and an irrational rotation number of constant type (i.e., coefficients in the continued fraction expansion are bounded). Any such homeomorphism has a unique invariant measure which is singular with respect to the Lebesgue measure. The Main Theorem of the paper states that singularities of the invariant measure are of Hölder type, and the Hausdorff dimension of the invariant measure is bounded away from 0 and 1.
Reviewer: V.A.Kaimanovich


37A99 Ergodic theory
28A78 Hausdorff and packing measures
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