We prove that non-trivial homoclinic classes of C r-generic flows are topo-logically mixing. This implies that given Λ a non-trivial C 1-robustly transitive set of a vector field X, there is a C 1-perturbation Y of X such that the continuation Λ Y of Λ is a topologically mixing set for Y. In particular, robustly transitive flows become topologically mixing after C 1-perturbations. These results...

We extend the results of Walters on the uniqueness of invariant measures with maximal entropy on compact groups to an arbitrary locally compact group. We show that the maximal entropy is attained at the left Haar measure and the measure of maximal entropy is unique.

We show that keeping only the topologically trivial contribution to the average of a class function on U (N) amounts to integrating over its algebra. The goal is reached first by decompactifying an expansion over the instanton basis and then directly, by means of a geometrical procedure. Keywords: Yang-Mills in two dimensions, invariant integration over groups and related algebras.