# Tanaka continued fractions and matching

In this talk we will first show that, for the Ito Tanaka continued fractions, matching holds almost everywhere. We do so by exploiting a relation between the orbit of the endpoints of the domain. In the second part we will try to adapt this proof for another family of continued fractions named the (N,\alpha)-continued fractions. This turns out to be difficult. Can we overcome these difficulties? The first part is joint work with Wolfgang Steiner and Carlo Carminati. The second part is joint work with Cor Kraaikamp.

This talk is part of the Topology and Dynamics Seminar series.