Barge, HéctorWójcik, K.2023-06-172023-06-1720171230-342910.12775/TMNA.2017.034https://hdl.handle.net/20.500.14352/18493In this paper we study a Mayer-Vietoris kind of formula for the fixed point index of maps of ENR triplets f : (X;X1,X2) → (X;X1,X2) having compact fixed point set. We prove it under some suitable conditions. For instance when (X;X1,X2) = (En;En+,En −). We use these results to generalize Poincar´e-Bendixson index formula for vector fields to continuos maps having a sectorial decomposition, to study the fixed point index i(f, 0) of orientation preserving homeomorphisms of E2 + and (E3;E3 +,E3 −) and the fixed point index in the invariant subspace.engjournal articlehttps://projecteuclid.org/euclid.tmna/1506477634https://projecteuclid.org/open access517.9Fixed point indexBrouwer degreeSectorial decompositionProper pairIsolated invariant set.Ecuaciones diferenciales1202.07 Ecuaciones en Diferencias