English

Darboux polynomials and global phase portraits for the D_2 vector field

Dynamical Systems 2018-08-14 v2

Abstract

We study a vector field of R^3 equivariant under the D_2 symmetry group, called "the D_2 field" in the literature. We construct the complete list of Darboux polynomials for it, solving the partial differential equation defining them. We also use these polynomials to comment on its global qualitative behaviour. This is meant to be a first step towards the comparison of vector fields based on the module generated by their Darboux polynomials.

Keywords

Cite

@article{arxiv.1804.01854,
  title  = {Darboux polynomials and global phase portraits for the D_2 vector field},
  author = {Kostas Katsios and Stavros Anastassiou},
  journal= {arXiv preprint arXiv:1804.01854},
  year   = {2018}
}

Comments

10 pages

R2 v1 2026-06-23T01:14:58.437Z