Convergence versus integrability in Poincare-Dulac normal form

Details Convergence versus integrability in Poincare-Dulac normal form Convergence versus integrability in Poincare-Dulac normal form

2001-05-23

arxiv.org/abs/math/0105193v2

Mathematics

Dynamical Systems

2nd version, substantial revision, new title

Scientific paper

We show that, to find a Poincare-Dulac normalization for a vector field is the same as to find and linearize a torus action which preserves the vector field. Using this toric characterization and other geometrical arguments, we prove that any local analytic vector field which is integrable in the non-Hamiltonian sense admits a local convergent Poincare-Dulac normalization. These results generalize the main results of our previous paper from the Hamiltonian case to the non-Hamiltonian case. Similar results are presented for the case of isochore vector fields.

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