6533b830fe1ef96bd1297b13
RESEARCH PRODUCT
Generalised power series solutions of sub-analytic differential equations
Mickaël MatusinskiJean-philippe Rolinsubject
Power seriesMathematics::Dynamical Systems[ MATH.MATH-CA ] Mathematics [math]/Classical Analysis and ODEs [math.CA]Differential equationHigh Energy Physics::Lattice010102 general mathematicsMathematical analysis06 humanities and the artsGeneral Medicine[MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA]0603 philosophy ethics and religion01 natural sciencesDimension (vector space)060302 philosophyVector fieldFinitely-generated abelian group0101 mathematicsAsymptotic expansionTrajectory (fluid mechanics)Mathematicsdescription
Abstract We show that if a solution y ( x ) of a sub-analytic differential equation admits an asymptotic expansion ∑ i = 1 ∞ c i x μ i , μ i ∈ R + , then the exponents μ i belong to a finitely generated semi-group of R + . We deduce a similar result for the components of non-oscillating trajectories of real analytic vector fields in dimension n. To cite this article: M. Matusinski, J.-P. Rolin, C. R. Acad. Sci. Paris, Ser. I 342 (2006).
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2006-01-01 |