Recently, P. Sarnak proposed to study the dynamical system
determined
by the arithmetic Moebius function $\mu:\N\to\{-1,0,1\}$. It has a natural
factor determined
by the characteristic function of the set of square-free numbers. This
system has positive
topological entropy and is not uniquely ergodic. The natural question
is whether this system
is intrinsically ergodic, i.e. has a unique invariant measure with
maximal entropy.
During the talk it will be shown that all B-free systems are
intrinsically ergodic.
The talk is based on a joint work with J. KuĊaga-Przymus and B. Weiss.