Composite Asymptotic Expansions and Difference Equations

• Published in: Revue Africaine de Recherche en Informatique et Mathématiques Appliquées Vol. 20 - 2015 - Special...; pp. 63 - 93
• Main Authors: Fruchard, Augustin, Schäfke, Reinhard
• Format: Journal Article
• Language: English
• Published: African Society in Digital Science 01.08.2015
• Subjects: Computer Science; Mathematics; Gevrey asymptotic; asymptotique Gevrey; Écalle-Voronin invariant; composite asymptotic expansion; coordonnée de Fatou; développement asymptotique combiné; invariant d'Écalle-Voronin; Équation aux différences à petit pas; Difference equation with small step size; Fatou coordinate

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...