Mathematics

Nakada’s α-expansions move from the regular continued fractions (α = 1), Hurwitz singular continued fractions (obtained at α =(-1+\sqrt{5})/2 ), and nearest integer continued fractions (α=1/2), to more unusual cases for α less than sqrt{2}-1. This talk will look at similar continued fraction expansions with odd partial quotients. I will describe how restricting the parity of the partial quotients changes the Gauss map and natural extension domain. This is joint work with Florin Boca as well as Yusef Hartono, Cor Kraaikamp, and Niels Langeveld.