Sturmian words, β-shifts, and transcendence

AbstractConsider the minimal β-shift containing the shift space generated by a given Sturmian word. In this paper we characterize such β and investigate their combinatorial, dynamical and measure-theoretical properties and prove that such β are transcendental numbers

The natural extensions of beta-transformations which generalize baker's transformations

We consider the natural extensions of beta-transformations. For some specific beta, the extensions can be viewed as generalized baker's transformations, i.e. they flatten and stretch and then cut and stack a two-dimensional domain. This paper characterizes such beta and studies their properties.