University of Birmingham > Talks@bham > Topology and Dynamics seminar > Specification and Synchronisation for unique expansions

Specification and Synchronisation for unique expansions

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If you have a question about this talk, please contact Robert Leek.

Given a positive integer M and q in (1,M+1] we study expansions in base q for real numbers over the alphabet {0,...,M}. In particular, we study some dynamical properties of a natural occurring subshift related to unique expansions in such base q known as symmetric lexicographic subshift. During the talk we will give a characterisation of the set of q’s such that such subshift has the specification property as well as the set of q’s such that such subshift is synchronised. We relate our results to those shown by Schmeling in (Ergodic Theory and Dynamical Systems, 17:675—694, 6 1997) in the context of greedy expansions in base q.

This talk is part of the Topology and Dynamics seminar series.

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