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

Discrete orbits and special subgroups of $\Diff$