q-BOREL-LAPLACE SUMMATION FOR q-DIFFERENCE EQUATIONS WITH TWO SLOPES

Ce papier a été initialement écrit sous le titre suivant : "Computing Bugeaud's solutions of q-difference equations with a q-Borel-Laplace summation"International audienceIn this paper, we consider linear q-difference systems with coefficients that are germs of meromorphic functions, with Newton polygon that has two slopes. Then, we explain how to compute similar meromorphic gauge transformations than those appearing in the work of Bugeaud, using a q-analogue of the Borel-Laplace summation