Frank Trujillo (Centre de Recerca Matemàtica, Barcelona) -- On invariant measures of circle maps with breaks

Attention, jour et heure inhabituels.

By a classical theorem of Denjoy, any sufficiently regular piece-wise smooth circle homeomorphism with finitely many branches (often called a circle homeomorphism with breaks) and irrational rotation number is topologically conjugated to an irrational circle rotation. In particular, it admits a unique invariant probability measure.

We will discuss dimensional properties of this measure and show that, generically, this unique invariant probability measure has zero Hausdorff dimension. To encode this generic condition, we consider piece-wise smooth homeomorphisms as generalized interval exchange transformations of the interval and rely on the notion of combinatorial rotation number