English

Asymptotic expansions of characteristic orbits of planar real analytic vector fields

Dynamical Systems 2026-03-09 v1

Abstract

The well-known Newton-Puiseux Theorem states that each real branch of a planar real analytic curve admits a Puiseux expansion. We generalize this result to characteristic orbit of an isolated singularity of a planar real analytic vector field and prove that each characteristic orbit has a `power-log' expansion.

Keywords

Cite

@article{arxiv.2603.06100,
  title  = {Asymptotic expansions of characteristic orbits of planar real analytic vector fields},
  author = {Jun Zhang},
  journal= {arXiv preprint arXiv:2603.06100},
  year   = {2026}
}

Comments

13 pages, 1 figure