Coboundaries and eigenvalues of finitary S-adic systems

Abstract: An S-adic system is a shift space obtained by performing an infinite composition of morphisms defined over possibly different finite alphabets. It is said to be finitary if these morphisms are taken from a finite set. S-adic systems are a generalization of substitution shifts. In this talk we will discuss spectral properties of finitary S-adic systems. Our departure point will be a theorem by B. Host which characterizes eigenvalues of substitution shifts, and where coboundaries appear as a key tool. We will introduce the notion of S-adic coboundaries and present some results which show how they are related with eigenvalues of S-adic systems. We will also present some applications of our results to constant-length finitary S-adic systems.

This is joint work with Valérie Berthé and Reem Yassawi.

dynamical systemsnumber theory

Audience: researchers in the topic

( paper | slides )

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One World Numeration seminar

Series comments: Description: Online seminar on numeration systems and related topics

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