Title: On the dynamics of finte topological rank Cantor minimal systems
Speaker: Alejandro Maass
Speaker Info: University of Chile
Brief Description:
Special Note:
Abstract:
The study of minimal Cantor systems became very relevant with the work in the 1990s by Giordano, Putnam and Skau on the characterization of orbital equivalence using algebraic properties of Bratteli-Vershik diagrams. Relevant classes are substitutive, linearly recurrent or finite topological rank systems. Since the 1990s these structures have been key to characterize classes of systems and their factors (Hedlund-Morse-like structural properties), to describe dynamical aspects such as the spectrum of such systems (continuous and measurable eigenvalues), the group of automorphisms or to understand rigidity properties, among many. On the other hand, from Downarowicz-Maass result one can establish that in the case of finite topological rank that Cantor minimal systems are subshifts or odometers, which allows to transit into the world of S-adic systems and to transfer many ideas from the world of Bratteli-Vershik diagrams. In this talk we will focus on establishing this relation, in particular for low complexity (non-superlinear) systems, and on describing recently established dynamical properties: eigenvalues of finite rank minimal Cantor systems, group of automorphisms, rigidity properties, ….Date: Tuesday, October 31, 2023