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M Handel has proved in [Topology 38 (1999) 235--264] a fixed point theoremfor an orientation preserving homeomorphism of the open unit disk, that may beextended to the closed disk and that satisfies a linking property of orbits. Wegive here a new proof of Handel's fixed point theorem, based on Brouwer theoryand some plane topology arguments. We will slightly improve the theorem byproving the existence of a simple closed curve of index 1. This index resultwas known to be true under an additional hypothesis and has been used bydifferent authors (J Franks [NYJM 2 (1996) 1--19, Trans.AMS 348 (1996)2637--2662] S Matsumoto [Topol. Appl. 104 (2000) 191--214]) to studyhomeomorphisms of surfaces.

Une nouvelle preuve du theoreme de point fixe de Handel