We discuss the local dynamics of a subgroup of Diff(C^2,0) possessing locally
discrete orbits as well as the structure of the recurrent set for more general
groups. It is proved, in particular, that a subgroup of Diff(C^2,0) possessing
locally discrete orbits must be virtually solvable. These results are of
considerable interest in problems concerning integrable systems.Comment: The first version of this paper and "A note on integrability and
finite orbits for subgroups of Diff(C^n,0)" are an expanded version of our
paper "Discrete orbits and special subgroups of Diff(C^n,0)". An intermediate
version re-submitted to the journal on March 2015 is available at
http://www.fep.up.pt/docentes/hreis/publications.htm where there is also a
comparison between these 3 version