Dynamical behaviour of alternate base expansions

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• Karma Dajani (Utrecht University)
• Thursday 11 February 2021, 15:00-16:00
• Zoom.

If you have a question about this talk, please contact David Craven.

We consider a generalisation of the β-expansion by applying cyclically the bases β₀,..., β_p-1. We refer to the resulting expansion as an (alternate base) β-expansion. Just as in the case of the classical β-expansion one has typically uncountably many expansions. We concentrate first on the greedy expansion, we introduce a dynamical system generating them and study its ergodic properties. We also compare the alternate base β-expansion with the greedy β_p-1... β₀-expansion with digits in some special set, and characterise when these expansions are the same. We end by introducing the lazy expansion and show that the dynamical system underlying such expansions is isomorphic to the greedy counterpart.

This is joint work with E. Charlier, and C. Cisternino.

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

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• Topology and Dynamics seminar
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