English

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

Classical Analysis and ODEs 2009-05-19 v1

Abstract

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.

Keywords

Cite

@article{arxiv.0905.2884,
  title  = {The return map for a planar vector field with nilpotent linear part: a direct and explicit derivation},
  author = {Rodica D. Costin},
  journal= {arXiv preprint arXiv:0905.2884},
  year   = {2009}
}

Comments

11 pages

R2 v1 2026-06-21T13:03:23.207Z