Dan Rust (Bielefeld)

Beyond primitivity for substitutions

Abstract:
Primitive substitutions are a key object of study in symbolic dynamics,
and for good reason. Primitivity of the substitution affords some
wonderful properties that make their analysis ameanable to a variety of
techniques from combinatorics, topological dynamics and ergodic theory.
Our goal will be to show that dropping the primitivity assumption does
not always complicate matters beyond comprehension. For some aspects,
such as their topological analysis, much weaker conditions suffice, in
order for the classical theory to be extended. We will introduce a
property called 'tameness' which generalises primitivity, and indicate
how parts of the classical theory are preserved or altered under the
tameness assumption.

(Joint work with Greg Maloney)

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