The Borel map in locally integrable structures

Given a locally integrable structure [Formula: see text] over a smooth manifold [Formula: see text] and given [Formula: see text] we define the Borel map of[Formula: see text] atp as the map which assigns to the germ of a smooth solution of [Formula: see text] at p its formal Taylor power series at p. In this work we continue the study initiated in Barostichi et al. (Math. Nachr. 286(14–15):1439–1451, 2013), Della Sala and Lamel (Int J Math 24(11):1350091, 2013) and present new results regarding the Borel map. We prove a general necessary condition for the surjectivity of the Borel map to hold and also, after developing some new devices, we study some classes of CR structures for which its surjectivity is valid. In the final sections we show how the Borel map can be applied to the study of the algebra of germs of solutions of [Formula: see text] at p.