Three Zutot

Abstract

Three topics in dynamical systems are discussed. In the first two sections we solve some open problems concerning, respectively, Furstenberg entropy of stationary dynamical systems, and uniformly rigid actions admitting a weakly mixing fully supported invariant probability measure. In the third section we provide a new example that displays some unexpected properties of strictly ergodic actions of non-amenable groups.

The paper has been withdrawn because the statement, in the first zuta,that the product measure ν_t is stationary is wrong. This means that the proof of the main result of this part, as presented, is not valid