The first return map for planar vector fields with nilpotent linear part with a center or a focus

Details The first return map for planar vector fields with nilpotent linear part with a center or a focus The first return map for planar vector fields with nilpotent linear part with a center or a focus

2009-05-20

arxiv.org/abs/0905.3316v1

Mathematics

Classical Analysis and ODEs

15 pages

Scientific paper

The return map for planar vector fields with nilpotent linear part (having a
center or a focus and under an assumption generically satisfied) is found as a
convergent power series 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 built with algebraic functions.

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