Summability of canard-heteroclinic saddle connections

Abstract

For a given (real analytic) slow-fast system {(x) over dot = epsilon f(x, y, epsilon) (y) over dot =g(x, y, epsilon), that admits a slow-fast saddle and that satisfies some mild assumptions, the Borel-summability properties of the saddle separatrix tangent in the direction of the critical curve are investigated: 1-summability is shown. It is also shown that slow-fast saddle connections of canard type have summability properties, in contrast to the typical lack of Borel-summability for canard solutions of general equations. (C) 2016 Elsevier Inc. All rights reserved.