Research objectives and content
The main purpose of my research project is to deepen my knowledge on the orbit structureOf continuous Zd-actions on Cantor spaces. I will mainly focus my attention to substitutive Z2-subshifts. First I would like to find 'good' Bratteli-Vershik models for these subshifts,i.e Bratteli-Vershik models where the dynamic can be encoded, then to characterize these Z2-subshifts with respect to their Bratteli-Vershik models. This work would certainly lead to know whether substitutive Z2-subshifts are orbit equivalent to substitution Z-subshift or not. Moreover if I could describe the dimension groups of substitutive Z2-subshifts I expect a very short proof of the so-called Cobham-Semenov Theorem, already proved,and to generalize this result to Bertrand numeration systems. This theorem lies between theory of automaton and arithmetic. This would be a very astonishing application of the Bratteli diagrams and of the dimension groups.
Training content (objective, benefit and expected impact)
The theory of C*-algebras is closely related to the orbit equivalence relation hence I would like to be introduced to its key concepts. Links with industry / industrial relevance (22)