Title: Resurgence of inner solutions for perturbations of the
McMillan map

Authors: P. Martín, T. M. Seara, D. Sauzin

Abstract: A sequence of “inner equations” attached to certain
perturbations of the McMillan map was considered in [MSS09],
their solutions were used in that article to measure an
exponentially small separatrix splitting. We prove here all the
results relative to these equations which are necessary to
complete the proof of the main result of [MSS09]. The present
work relies on ideas from resurgence theory: we describe the
formal solutions, study the analyticity of their Borel
transforms and use ´Ecalle’s alien derivations to measure the
discrepancy between different Borel-Laplace sums.