Il Prof. Pierre Liardet, dell'Universite' de Provence, (Marsiglia) , sara' ospite del Dipartimento nella settimana 7/4/08- 11/4/08. Terra' un seminario dal titolo "The dynamical structure of chaîned flows and applications to uniform distribution of digital block functions". il giorno 7/4/08, alle ore 15.30, in Sala Seminari. Tutti gli interessati sono cordialmente invitati ad intervenire
******************************************************************************************************* ABSTRACT.
We investigate the dynamical structures of flows arising from arithmetic se- quences, called chain sequences, computed from digital expansion of integers in a given base. A classical example in base 2 is the sequence n → αsw (s) mod 1 where α is irrational and sw (n) is the number of occurrences of the binary word w (not written with the only digit 0) in the binary expansion of n. We distinguish contrac- tive and non contractive chained sequences. In the above example, the sequence is contractive if w is of length ≥ 2 and non contractive but completly 2-additive mod 1 if w = 1. The flows associated to such sequences are minimal and uniquely ergodic. In the contractive case the flow is metrically conjugated to a skew product. The non contractive case is more intricated but analogous. In both cases the spectral type of the underlying dynamical system is classified and applications to uniform distribution are given. ***************************************************************************************************************