Weak mixing and eigenvalues for arnoux-rauzy sequences - Cassaigne, Julien; Ferenczi, Sébastien; Messaoudi, Ali [UNESP] (Cellule MathDoc/Centre Mersenne, 2008)
We define by simple conditions two wide subclasses of the socalled Arnoux-Rauzy systems; the elements of the first one share the property of (measure-theoretic) weak mixing, thus we generalize and improve a counterexample to the conjecture that these systems are codings of rotations; those of the second one have eigenvalues, which was known hitherto only for a very small set of examples.
Keywords: Complexity; Eigenvalues; Symbolic dynamics