University of Birmingham > Talks@bham > Topology and Dynamics seminar > The Ellis semigroup of generalized Morse sequences

The Ellis semigroup of generalized Morse sequences

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

The Ellis semigroup of a dynamical system is a very useful tool. However, there are very few concrete / understandable examples of Ellis semigroups of specific dynamical systems. In 1997, Haddad and Johnson prove that the Ellis semigroup of any generalised Morse sequence has four minimal idempotents. They base their proof on a proposition stating that any IP cluster point along an integer sequence can be represented as an IP cluster point along either a wholly positive or wholly negative integer IP sequence. In this talk, we provide large class of counterexamples to that proposition. We also provide a proof of their main theorem via the algebra of the Ellis semigroup, and show how it can be extended to a larger class of substitution systems over arbitrary (not only binary) finite alphabets.

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

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