Skew-product for group-valued edge labellings of Brateli diagrams. (English) Zbl 1231.37008

El Kacimi, A.; Parthasarathy, R.

Publ. Mat., Barc. 53, No. 2, 329-354 (2009).

Summary: We associate a Cantor dynamical system to a non-properly ordered Bratteli diagram. Group valued edge labellings \(\lambda\) of a Bratteli diagram \(B\) give rise to a skew-product Bratteli diagram \(B(\lambda)\) on which the group acts. The quotient by the group action of the associated dynamics can be a nontrivial extension of the dynamics of \(B\). We exhibit a Bratteli diagram for this quotient and construct a morphism to \(B\) with unique path lifting property. This is shown to be an isomorphism for the dynamics if a property “loops lifting to loops” is satisfied by \(B(\lambda )\to B\).

MSC:

37B10	Symbolic dynamics
37B05	Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.)
54H20	Topological dynamics (MSC2010)

Keywords:

Cantor minimal system; Bratteli diagram; substitutional system

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