ÉQUATIONS DIFFÉRENTIELLES À COEFFICIENTS DANS DES CORPS DE SÉRIES GÉNÉRALISÉES.

Mickael Matusinski 1
1 Géométrie
IMB - Institut de Mathématiques de Bourgogne
Abstract : We express the connection between the support of some equations and those of generalized series solutions. On the one hand we prove that any real power series solution of a sub-analytic differential equation belong to a lattice (i.e. an additive sub semi-group of positive reals). On the other hand we consider the field Mr of series with well-ordered support included in the Hahn product Hr with finite rank r (i.e. the lexicographic product of r copies of the reals). We equip Mr with a "Hardy type" derivation and define some well-ordered sets T1, ..., Tr such that : for all equation F(y,...,y(n))=0 with F in Mr[[Y0,...,Yn]] and whose support Supp F is a well-ordered subset of Hr, and for all solution y0 in Mr with v(y0(i))> (0,...,0) for i=0,...,n, then the exponents of y0 belong to a positive well-ordered subset of Hr obtained from Supp F, T1, ..., Tr by a finite number of elementary transformations.
Document type :
Theses
Mathematics. Université de Bourgogne, 2007. French
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https://tel.archives-ouvertes.fr/tel-00366152
Contributor : Mickaël Matusinski <>
Submitted on : Friday, March 6, 2009 - 1:34:22 AM
Last modification on : Wednesday, October 29, 2014 - 1:23:01 PM

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  • HAL Id : tel-00366152, version 1

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Mickael Matusinski. ÉQUATIONS DIFFÉRENTIELLES À COEFFICIENTS DANS DES CORPS DE SÉRIES GÉNÉRALISÉES.. Mathematics. Université de Bourgogne, 2007. French. <tel-00366152>

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