The return map for a planar vector field with nilpotent linear part: a direct and explicit derivation

Details The return map for a planar vector field with nilpotent linear part: a direct and explicit derivation The return map for a planar vector field with nilpotent linear part: a direct and explicit derivation

2009-05-18

arxiv.org/abs/0905.2884v1

Mathematics

Classical Analysis and ODEs

11 pages

Scientific paper

Using a direct approach the return map near a focus of a planar vector field
with nilpotent linear part is found as a convergent power series which is a
perturbation of the identity and whose terms can be calculated iteratively. The
first nontrivial coefficient is the value of an Abelian integral, and the
following ones are explicitly given as iterated integrals.

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