Universiteit Utrecht

Department of Mathematics

Expansions and extensions

Charlene Kalle

24 June 2009

Beta-expansions with arbitrary digits are number expansions where the base beta can be any real number bigger than 1 and with digits taken from an arbitrary set of real numbers. Under some mild conditions on the digit set, every number in a certain interval has such an expansion and there are transformations that give these expansions by iteration. In this talk we will define such transformations and discuss some measure theoretic and ergodic properties of their dynamical systems.

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Alexandra Babenko