English

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

Classical Analysis and ODEs 2009-05-21 v1

Abstract

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.

Keywords

Cite

@article{arxiv.0905.3316,
  title  = {The first return map for planar vector fields with nilpotent linear part with a center or a focus},
  author = {Rodica D. Costin},
  journal= {arXiv preprint arXiv:0905.3316},
  year   = {2009}
}

Comments

15 pages

R2 v1 2026-06-21T13:04:16.993Z