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Normal forms of invariant vector fields under a finite group action.

Federico Sánchez-Bringas (1993)

Publicacions Matemàtiques

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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 C and on the group of germs of holomorphic diffeomorphisms of (C, 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.