Title: The entropy of $\alpha$-continued fractions
Speaker: Giulio Tiozzo (Harvard)
Abstract: We consider a one-parameter family of interval maps arising from generalized continued fraction expansions known as $\alpha$-continued fractions. For such maps, we investigate the behaviour of Kolmogorov-Sinai entropy as a function of the parameter; we will discuss numerical evidence that this function has a self-similar structure, as well as theoretical results about its regularity.