Rigid Germs, the Valuative Tree, and Applications to Kato Varieties

This thesis deals with specific featuresof the theory of holomorphic dynamics in dimension 2 and then sets out to studyanalogous questions in higher dimensions, e.g. dealing with normal forms forrigid germs, and examples of Kato 3-folds.

The local dynamics of holomorphic mapsaround critical points is still not completely understood, in dimension 2 orhigher, due to the richness of the geometry of th...