Zeros of Bouligand-Nagumo Fields, Flow-Invariance and the Bouwer Fixed Point Theorem

Abstract

**Please note that the full text is embargoed** ABSTRACT: Mainly, in this paper we prove that if D is a convex compact of Rn, then the Brouwer fixed point property of D is equivalent to the fact that every Bouligand-Nagums vector field on D, has a zero in D. Using a version of this result on a normed space, as well as the Day [9] and Dugundji [10] theorems, we give a new proof to the fact that in every infinite dimensional Banach space X, there exists a continuous function from the closed unit ball B (of X) into B, without fixed points in B. We also show that our results include several classical results. Some applications to Flight Mechanics are given, too.