Newton's method for solutions of quasi-Bessel differential equations.
Non linearizable holomorphic dynamics having an ancountable number of symmetries.
Normal forms of invariant vector fields under a finite group action.
Let Γ be a finite subgroup of GL(n, C). This subgroup acts on the space of germs of holomorphic vector fields vanishing at the origin in Cn and on the group of germs of holomorphic diffeomorphisms of (Cn, 0). We prove a theorem of invariant conjugacy to a normal form and linearization for the subspace of invariant germs of holomorphic vector fields and we give a description of this type of normal forms in dimension n = 2.