  The local topological dynamics of subgroups of ${\rm Diff} ({\mathbb C^n},
0)$, with special emphasis on ${\rm Diff} ({\mathbb C^2}, 0)$, is discussed
with a view towards integrability questions. It is proved in particular that a
subgroup of ${\rm Diff} ({\mathbb C^2}, 0)$ possessing locally finite orbits is
necessarily solvable. Other results and examples related to higher-dimensional
generalizations of Mattei-Moussu's celebrated topological characterization of
integrability are also provided. These examples also settle a fundamental
question raised by the previous work of Camara-Scardua.
