Possible entropy functions (Q1424039)

The authors describe all possible entropy functions (i.e., a function assigning to invariant probability measures on a topological dynamical system their entropy), when the dynamical system is minimal. It is also shown that such a function is realizable on an expansive dynamical system. The construction of the dynamical system is using minimal, almost onto 1-1 extensions over a rotation of a group of \(p\)-adic integers.