# Generalised power series solutions of sub-analytic differential equations

Abstract : We show that if a solution $y(x)$ of a sub-analytic differential equation admits an asymptotic expansion $\sum_{i=1}^{\infty} c_i x^{\mu_i}$ with $\mu_i\in\mathbb{R}_+$, then the exponents $\mu_i$ belong to a finitely generated semi-group of $\mathbb{R}_+$. We deduce a similar result for the components of non-oscillating trajectories of real analytic vector fields in dimension n.
Document type :
Journal articles

https://hal.archives-ouvertes.fr/hal-00947120
Contributor : Mickaël Matusinski <>
Submitted on : Thursday, January 26, 2017 - 10:08:13 AM
Last modification on : Tuesday, November 6, 2018 - 7:52:03 PM

### Citation

Mickaël Matusinski, Jean-Philippe Rolin. Generalised power series solutions of sub-analytic differential equations. Comptes Rendus Mathématique, Elsevier Masson, 2006, 342 (2), pp.99 - 102. ⟨10.1016/j.crma.2005.11.005⟩. ⟨hal-00947120⟩

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