Frank Trujillo (University of Zürich, Switzerland)

Hausdorff dimension for invariant measures of critical circle maps

Critical circle maps are a family of smooth circle homeomorphisms whose derivatives vanish at a non-empty finite set. Any sufficiently regular critical circle map with an irrational rotation number can be continuously conjugated to an irrational rotation. Furthermore, its unique invariant measure is singular with respect to the Lebesgue measure on the circle. In this talk, I will recall the notion of the Hausdorff dimension of a measure and give explicit bounds of its value for invariant measures of critical circle maps. As we shall see, these bounds will depend only on the arithmetic properties of the rotation number.