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The index of Lyapunov stable fixed points in two dimensions. (English) Zbl 0811.34018
Let \(U \subset R^ 2\) be an open and connected set, \(0 \in U\), \(f:U \to R^ 2\) be a continuous, one-to-one and orientation-preserving mapping, \(f(0) = 0\). If 0 is stable and isolated as a fixed point of \(f\), then the fixed point index is equal to one. Applications to differential equations are given.
Reviewer: M.Bartušek (Brno)

MSC:
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
47H11 Degree theory for nonlinear operators
34D20 Stability of solutions to ordinary differential equations
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