From greedy to lazy expansions and their driving dynamics (Q1857371)

There are many ways to develop a real number in \([0,1)\) using a non-integer base \(\beta>1\). Here it is shown that the `greedy' and `lazy' expansions are isomorphic in the sense of ergodic theory. In addition, a family of expansions that interpolate between the two expansions is found, and it is shown that these expansions are determined by maps of the form \(x\mapsto\beta x+\alpha\) mod \(1\).