Felipe Arbulu (Jules Vernes University Amiens)

Title: Spectral analysis of some classes of S-adic subshifts

Abstract: Motivated by systems of geometric nature, symbolic dynamics arose as an
attempt to study dynamical systems by means of discretizing space as
well as time.
In most cases, words in the natural coding of orbits can be expressed as
the images of a composition of morphisms between finitely generated
monoids.
The systems thus generated are called S-adic subshifts and form a rich
family that has been intensively studied from different perspectives
such as combinatorics on words, ergodic theory and Diophantine
approximation.

In the first part of this talk, I will explain how the idea of encoding
orbits by means of morphisms can be used to study the dynamical
properties of rank-one subshifts with bounded spacers: we compute their
(continuous and measurable) eigenvalues and their (weak and strong)
orbit equivalence classes.
Next, we restrict our study to constant length S-adic subshifts, a class
that includes minimal Toeplitz subshifts.
We characterize within this class the spectral properties of the factor
maps onto the maximal equicontinuous topological factors by means of
coincidences.
Finally, we will see how the notion of coincides plays a role in the
study of rigidity for substitution subshifts and constant length S-adic
subshifts.