We studied the local dynamics of a subgroup of Diff(C2,0) possessing locally discrete orbits proving, in particular, that such subgroup must be virtually solvable. We also studied the structure of the recurrent set for more general groups. More precisely, given a non-solvable subgroup of Diff1(C2,0), we proved the existence of a neighbourhood U of the origin such that the set of points on U that fail to be recurrent has null Lebesgue mesure.

Study of the dynamics of non-solvable subgroups of Diff1(C2,0): basins of attraction and existence of vector fields whose flow is a limit of a sequence of elements of the group.

We showed that holomorphic vector fields on (C3,0) have separatrices provided that they are embedded in a rank 2 representation of a two-dimensional Lie algebra.