Asymptotic expansions of characteristic orbits of planar real analytic vector fields

Jun Zhang

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arXiv · 2603.06100

Asymptotic expansions of characteristic orbits of planar real analytic vector fields

Jun Zhang

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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.

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Jun Zhang. 2026-03-06. Asymptotic expansions of characteristic orbits of planar real analytic vector fields. https://arxiv.org/abs/2603.06100

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