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RESURGENCE OF INNER SOLUTIONS FOR PERTURBATIONS OF THE MCMILLAN MAP

A sequence of "inner equations" attached to certain perturbations of the 
 McMillan map was considered in [5], 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 [5]. 
 
 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.