Recent advances in the metric theory of θ-expansions

Abstract

A survey of the metric theory of θ-expansions discussed in [1, 5, 6, 7] is given. The limit properties of these expansions have been studied. Using a Wirsing-type approach to the Perron-Frobenius operator of the generalized Gauss map under its invariant measure we find a near-optimal solution to the Gauss-Kuzmin-L'evy problem for θ-expansions.