Jisom

Planning :

9h30-12h (30 mn de pause) Yousuke Ohyama (Osaka university)

Titre : Asymptotic analysis on the Painlevé equations: Boutroux 100

Résumé : A hundred years has passed since Pierre Boutroux studied global asymptotics of the Painleve equations. In these 25 years, many researchers have been studied Boutroux’s analysis from a modern viewpoint. Painleve transcendents have three different types of asymptotic expansion: (1) power expansions around regular singular points, (2) exponential expansions around irregular singular points, (3) Global elliptic expansions. We will study these three types of expansions for a special Painleve equation using isomonodromic deformations. Reference: P. Boutroux, Recherches sur les transcendantes de M. Painleve et l’etude asymptotique des equations differentielles du second ordre, Ann. Sci. Ecole Norm. Sup. (3) 30, pp. 255–375; 31 (1914), pp. 99–159. ***

14h-16h30 (30 mn de pause) Takeshi Morita (Osaka university)

Titre: Connection problems on higher order linear q-difference equations

Résumé court : We study connection problems on higher order linear $q$-difference equations between around the origin and around the infinity. For simplicity, we deal with the third order $q$-difference equations. In the fundamental system of solutions around the origin, divergent basic hypergeometric series appear. We use the $q$-Borel-Laplace transformations to obtain the asymptotic expansion of these divergent series. Our conclusion also give examples of the $q$-Stokes coefficients.

Résumé long