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Thursday, September 6, 2018

**Abstract:** Nakada's $\alpha$-expansions interpolate between three classical continued fractions: regular (obtained at $\alpha=1$), Hurwitz singular (obtained at $\alpha$=little golden mean), and nearest integer (obtained at $\alpha$=1/2). This talk will consider $\alpha$-expansions in the situation where all partial quotients are asked to be odd positive integers. We will describe the natural extension of the underlying Gauss map and the ergodic properties of these transformations. This is joint work with Claire Merriman.