SEMINARIO DI DIPARTIMENTO
15:30-18:00, Sala Seminari (Dip. Matematica)
The dynamical structure of chaîned flows and applications to uniform distribution of digital block functions
Pierre Liardet (Universite' de Provence, (Marsiglia))



Abstract:
We investigate the dynamical structures of flows arising from arithmetic sequences, called chain sequences, computed from digital expansion of integers in a given base. A classical example in base 2 is the sequence n sw (s) mod 1 where 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 contractiveand non contractive chained sequences. In the above example, the sequence is contractive if w is of length 2 and non contractive but completly 2additive 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 spectraltype of the underlying dynamical system is classified and applications to uniform distribution are given.