ABSTRACT


From greedy to lazy expansions and their driving dynamics.
We study the ergodic properties of non-greedy expansions to a non-integer base $\beta >1$. We show that the so called lazy expansion is isomorphic to the greedy counterpart, and we exhibit (using a deterministic procedure) a new family of non-greedy expansions that are neither greedy nor lazy. We show that these are isomorphic to expansions generated by iterating maps of the form $Tx=\beta x+\alpha$ (mod 1). Finally, a random expansions to base $\beta$ is given, and completely analyzed for $\beta$ satisfying the equation $\beta^2-n\beta-k=0$ with $n\geq k$.
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Martijn Pistorius (pistorius@math.uu.nl)

Last Updated: November 19, 2001