Integral curves and Jacobian Conjecture

In this note, we are interested in the Jacobian Conjecture. Following the results of L.M.~Dru$\dot{\rm z}$kowski, we consider some vector fields depending on a certain \'etale polynomial map. From results of semialgebraic geometry with the consideration of some integral curves of these vector fields, we deduce that an \'etale polynomial endomorphism is a polynomial automorphism.