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Mayer-vietoris property of the fixed point index

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Barge, Héctor and Wójcik, K. (2017) Mayer-vietoris property of the fixed point index. Topological Methods in Nonlinear Analysis, 50 (2). pp. 643-667. ISSN 1230-3429

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Official URL: https://projecteuclid.org/euclid.tmna/1506477634


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Abstract

In 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.


Item Type:Article
Uncontrolled Keywords:Fixed point index; Brouwer degree; Sectorial decomposition; Proper pair; Isolated invariant set.
Subjects:Sciences > Mathematics > Differential equations
ID Code:47101
Deposited On:15 Feb 2019 12:18
Last Modified:18 Feb 2019 08:19

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