Corinna Ulcigrai

Renewal-type Limit Theorem for the Gauss map and continued fractions

In this paper we prove the following renewal-type limit theorem. Given an irrational

Mixing of asymmetric logarithmic suspension flows over interval exchange transformations

\alpha

Diagonal changes for surfaces in hyperelliptic components - A geometric natural extension of Ferenczi-Zamboni moves

in (0,1) and R>0, let

Non-ergodic

q_{n_R}

\mathbb{Z}

be the first denominator of the convergents of

-periodic billiards and infinite translation surfaces

\alpha

Beyond Sturmian sequences: coding linear trajectories in the regular octagon

which exceeds R. The main result in the paper is that the ratio

Weak Mixing in Interval Exchange Transformations of Periodic Type

q_{n_R}/R

Absence of mixing in area-preserving flows on surfaces

has a limiting distribution as R tends to infinity. The existence of the limiting distribution uses mixing of a special flow over the natural extension of the Gauss map.

Geodesic flow on the Teichmueller disk of the regular octagon, cutting sequences and octagon continued fractions maps

We consider suspension flows built over interval exchange transformations with the help of roof functions having an asymmetric logarithmic singularity. We prove that such flows are strongly mixing for a full measure set of interval exchange transformations.