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Integrable analytic vector fields with a nilpotent linear part. (English) Zbl 0835.58032
Summary: We study the normalization of analytic vector fields with a nilpotent linear part. We prove that such an analytic vector field can be transformed into a certain form by convergent transformations when it has a non-singular formal integral. We then prove that there are smoothly linearizable parabolic analytic transformations which cannot be embedded into the flows of any analytic vector fields with a nilpotent linear part.

MSC:
37G05 Normal forms for dynamical systems
37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems
32S65 Singularities of holomorphic vector fields and foliations
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