Non-stationary Markov partitions for Pisot cocycles
Aix-Marseille Université - Site St Charles
3, place Victor Hugo - case 39
13331 MARSEILLE Cedex 03
It is well known that there exist always Markov partitions for toral automorphisms.
We generalize this result when considering a two-sided sequence of toral automorphisms which are not necessarily the same.
This corresponds to deal with a so-called symbolic cocycle specified by a two-sided sequence of unimodular substitutions.
Under certain assumptions of special hyperbolicity of the cocycle, namely the Pisot assumption, we can construct explicit Markov partitions by using the geometric theory of Rauzy fractals. We explore in particular the connections with multi-dimensional continued fraction algorithms, and we apply our theory to the case of the Brun substitutions.
- Milton MINERVINO