Marta Magionni (Leiden)

Matching for a flipped family of alpha-continued fractions

Alpha-continued fractions were introduced in 1981 by Nakada as a family of interval maps depending on a parameter alpha. Since then, numerous studies have been done on the maps' metric and ergodic properties. In particular, the entropy has been studied as a function of alpha: explicit intervals on which it is constant, increasing or decreasing have been characterised by the matching index of alpha and 1-alpha. We present a natural counterpart to the alpha-continued fractions. For this new collection of maps, we show, in contrast with the former family, that the (Krengel) entropy is constant, and we describe the matching intervals through the regular continued fraction expansions of alpha.   

This is a joint work with Charlene Kalle, Niels Langeveld and Sara Munday.