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Journal articles
Composite Asymptotic Expansions and Difference Equations
Composite Asymptotic Expansions and Difference Equations
Abstract : Difference equations in the complex domain of the form y(x+ϵ)−y(x)=ϵf(y(x))/y(x) are considered. The step size ϵ>0 is a small parameter, and the equation has a singularity at y=0. Solutions near the singularity are described using composite asymptotic expansions. More precisely, it is shown that the derivative v′ of the inverse function v of a solution (the so-called Fatou coordinate) admits a Gevrey asymptotic expansion in powers of the square root of ϵ, denoted by η, involving functions of y and of Y=y/η. This also yields Gevrey asymptotic expansions of the so-called Écalle-Voronin invariants of the equation which are functions of epsilon. An application coming from the theory of complex iteration is presented.
Cited literature [6 references]
https://hal.inria.fr/hal-01320625
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Submitted on : Tuesday, May 24, 2016 - 11:01:20 AM
Last modification on : Thursday, July 9, 2020 - 8:25:48 AM
Contributor : Coordination Episciences Iam Connect in order to contact the contributor
Submitted on : Tuesday, May 24, 2016 - 11:01:20 AM
Last modification on : Thursday, July 9, 2020 - 8:25:48 AM
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vol.20.pp.63-93.pdf
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