Paulina Cecchi

University of Chile · Centro de Modelamiento Matemático (CMM)

An S-adic system is a symbolic dynamical system generated by iterating an infinite sequence of substitutions or morphisms, called a directive sequence. A finitary S-adic dynamical system is one where the directive sequence consists of morphisms selected from a finite set. We study eigenvalues and coboundaries for finitary recognizable S-adic dynami...

Dimension groups are complete invariants of strong orbit equivalence for minimal Cantor systems. This paper studies a natural family of minimal Cantor systems having a finitely generated dimension group, namely the primitive unimodular proper \({\mathcal {S}}\)-adic subshifts. They are generated by iterating sequences of substitutions. Proper subst...

We show that within any strong orbit equivalent class, there exist minimal subshifts with arbitrarily low superlinear complexity. This is done by proving that for any simple dimension group with unit $(G,G^+,u)$ and any sequence of positive numbers $(p_n)_{n\in\mathbb{N}}$ such that $\lim n/p_n=0$, there exist a minimal subshift whose dimension gro...

Dimension groups are complete invariants of strong orbit equivalence for minimal Cantor systems. This paper studies a natural family of minimal Cantor systems having a finitely generated dimension group, namely the primitive unimodular proper S-adic subshifts. They are generated by iterating sequences of substitutions. Proper substitutions are such...

In this work we study some dynamical properties of symbolic dynamical systems, with particular emphasis on the role played by the invariant probability measures of such systems. We approach the study of the set of invariant measures from a topological, combinatorial and geometrical point of view. From a topological point of view, we focus on the pr...

This paper studies balancedness for infinite words and subshifts, both for letters and factors. Balancedness is a measure of disorder that amounts to strong convergence properties for frequencies. It measures the difference between the numbers of occurrences of a given word in factors of the same length. We focus on two families of words, namely de...

This paper studies balancedness for infinite words and subshifts, both for letters and factors. Balancedness is a measure of disorder that amounts to strong convergence properties for frequencies. It measures the difference between the numbers of occurrences of a given word in factors of the same length. We focus on two families of words, namely de...