In this article we give necessary and sufficient conditions for a complex number to be a continuous eigenvalue of a minimal Cantor system. Similarly, for minimal Cantor systems of finite rank, we provide necessary and ...

It will be shown that every minimal Cantor set can be obtained as a projective limit of directed graphs. This allows to study minimal Cantor sets by algebraic topological means. In particular, homology, homotopy and ...

En 1992 M. Boshernitzan [6] presenta una condición suficiente para que los subshifts minimales sean únicamente ergódicos. Usando el concepto de factores simbólicos extendemos esta condición a sistemas minimales de Cantor. ...

We show that every uniquely ergodic minimal Cantor system is topologically orbit equivalent to the natural extension of a numeration scale associated to a logistic map.

In this paper we characterize measure-theoretical eigenvalues of Toeplitz Bratteli–Vershik minimal systems of finite topological rank which are not associated to a continuous eigenfunction. Several examples are provided ...

A well-known consequence of the ergodic decomposition theorem is that the space of invariant probability Measures of a topological dynamical system, endowed with the weak* topology, is a non-empty metrizable Choquet simplex. ...