Analysis, Geometry, and Dynamical Systems Seminar   RSS

17/12/2018, 15:00 — 16:00 — Room P4.35, Mathematics Building
Daniel Gonçalves, Universidade Federal de Santa Catarina, Brasil

Infinite alphabet ultragraph edge shift spaces: relations to $C^\ast$-algebras and chaos

We explain the notion of ultragraphs, which generalize directed graphs, and use this combinatorial object to define a notion of (one-sided) edge shift spaces (which, in the finite case, coincides with the edge shift space of a graph). We then go on to show that these shift spaces have some nice properties, as for example metrizability and basis of compact open sets. We examine shift morphisms between these shift spaces: we give an idea how to show that if two (possibly infinite) ultragraphs have edge shifts that are conjugate, via a conjugacy that preserves length, then the associated ultragraph $C^\ast$-algebras are isomorphic. Finally we describe Li-Yorke chaoticity associated to these shifts and remark that the results obtained mimic the results for shifts of finite type over finite alphabets (what is not the case for infinite alphabet shift spaces with the product topology).