Abstract
Abstract In this paper, we establish an ω + {\omega^{+}} -type index theory for paths in the general linear group GL + ( 2 ) {\mathrm{GL}^{+}(2)} . This is done by the complete homotopy classification for such paths. We also compare this index theory with the ω index theory for paths in the symplectic group Sp ( 2 ) {\mathrm{Sp}(2)} and obtain a generalization of Bott formula for iterated paths in GL + ( 2 ) {\mathrm{GL}^{+}(2)} . As applications, the minimal periodic solution problem and the linear stability of general differential systems are studied.
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