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Article Dans Une Revue Comptes Rendus. Mathématique Année : 2006

Generalised power series solutions of sub-analytic differential equations

Résumé

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.

Dates et versions

hal-00947120 , version 1 (26-01-2017)

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Citer

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