Dynamical study of continued fraction and its generalization

Abstract

It is conjectured that the length of continued fraction behaves asymptotically like a random variable with the Gaussian distribution. This conjecture was proved by Baladi and Vallee in an average sense by studying spectral properties of transfer operator associated with a dynamical system for the Gauss map on the unit interval. In the talk, we generalize their work to a skewed dynamical system and obtain spectral properties of the corresponding transfer operator. As results, we present some number theoretical applications. This is joint work with Jungwon Lee.