Abstract: We introduce a class of piecewise linear transformations that can be used to generate beta-expansions with arbitrary digits. Under some conditions on beta and the digit set, we can construct a natural extension for such a transformation, which allows us to get an invariant measure equivalent to Lebesgue for the original transformation. From the natural extension, we obtain a multiple tiling of a Euclidean space. For the classic greedy beta-transformation (Tx = beta x (mod 1)) the Pisot conjecture states that this construction gives a proper tiling for all Pisot numbers beta. We give an example of a double tiling, showing that this conjecture is no longer true in the more general setting.
Here is a link to the slides of Charlene Kalle’s talk
Location: room 611 of the Wiskunde building (campus De Uithof) Budapestlaan 6, Utrecht.
Date and time: Thursday, October 29, 2009 15:30-16:30. The lecture is preceded by coffee, tea, and cookies from 15.00 to 15.30 hour in the same room.
Schedule of the Utrecht math colloquium : Next term’s talks, This year's talks. Last year's talks. Guidelines for speakers.
Other math colloquia : TU Delft, Leiden, UvA Amsterdam, VU Amsterdam, Nijmegen.
Organisers : Gil Cavalcanti, Wilberd van der Kallen and Paul Zegeling