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