Dynamical Systems and Analysis Seminar - Dan Rust
| Dates: | 9 November 2026 |
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| Times: | 14:00 - 15:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Who is it for: | University staff, External researchers, Current University students |
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Speaker: Dan Rust (Open University)
Title: Substitution dynamical systems on compact alphabets
Abstract: Substitution subshifts over finite alphabets are some of the simplest and best-known dynamical systems with a huge amount of literature devoted to them. In contrast, substitutions on infinite alphabets have been far less well-studied. In this talk, I'll discuss the development of a framework for studying certain classes of these substitutions where one imposes a topology on the alphabet with respect to which the substitution is continuous. When that topology is compact and Hausdorff, there is a robust theory of their dynamics that can be developed, which mirrors the theory for finite alphabets, but with some important distinctions that I will highlight. Importantly, Perron-Frobenius theory is no longer sufficient to study invariant measures, and so the theory of positive operators on Banach lattices needs to be used instead. I'll also discuss some recent progress on the specific case of when the alphabet is countable, which can make some of these problems more tractable.
This is joint work with Neil Manibo, Jamie Walton and Raphael Henry.
Room: Frank Adams 1
Further information: https://personalpages.manchester.ac.uk/staff/yotam.smilansky/dynamics_analysis
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Frank Adams 1
Alan Turing Building
Manchester
