5 nov 2014 -- 15:30
Sala Conferenze, Collegio Puteano, Centro De Giorgi, Pisa
Seminari di Sistemi Dinamici Olomorfi, Pisa
Abstract.
In 1981, Hitoshi Nakada introduced a family of continued fraction maps, and studied their natural extensions. These are the Nakada alpha-expansions, which are defined for a parameter alpha between 0 and 1. These alpha-expansions played a key role in the revival of the interest in continued fraction expansions, and are up to today subject of thorough investigations. Using some extremely basic ideas called ‘insertions’ and ‘singularizations’ we will show that there is a strong relation between alpha-expansions for various values of alpha-expansions. In this talk I will show how far these ideas can be carried over, and how they can be used in other settings, e.g. for the so-called ‘Rosen fractions.’