abstract: In some problems of separatrix splitting it is important to match "outer" asymptotic expansions in a parameter away from a pole of the first approximation with "inner" expansions near that pole. The purpose of my lecture is to show how composite asymptotic expansions (studied in detail in FS) can help with this problem and even shed some new light on the expansions.
FS FruchardSchäfke, Composite asymptotic expansions. Lecture Notes in Mathematics, 2066.