Chaotic sets and Hausdorff dimension for Lüroth expansions

Abstract

Regular continued fraction expansions and Lüroth series of real numbers within the unit interval share several properties, although they are generated by different dynamical systems. Our research provides new similarities between both sets of expansions in terms of topological dynamics and Hausdorff dimension. In particular, we establish a complete analogue with the results of W. Liu, B. Li and S. Wang in [19,20] on the distal, asymptotic and Li-Yorke pairs for the Gauss map, in the case of the Lüroth transformation.