Title: The beta-transformation with a hole at 0
Abstract: An open dynamical system is a dynamical system with an open subset (the "hole") of the domain that must be avoided. One studies in particular the survivor set of points whose orbit never enters the hole. In this talk I will focus on an open dynamical system arising from the beta transformation on [0,1) with a hole (0,t). It was shown recently by Kalle, Kong, Langeveld and Li that the Hausdorff dimension of the survivor set, as a function of t, is a descending devil's staircase. Of particular interest is the critical value of t where this function reaches zero. I will discuss this question, as well as our current work toward proving an intriguing conjecture from the paper of Kalle et al. This is joint work with Derong Kong.