Actions of finitely generated groups and semigroups on a plane by means of isometries (Q1889633)

Let \(G\) be a countable finitely generated group or semigroup equipped with a fixed set of generators, e.g., a group of isometries of an affine Euclidean plane. The author studies conditions under which orbits of the action of the group \(G\) are uniformly distributed and gives a criterion for every orbit to be dense. Estimates for the time spent by an orbit is a compact set are obtained as well.