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Location of fixed points and periodic solutions in the plane

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  • An orientation-preserving homeomorphism of the plane having a two-cycle has also a fixed point. This result goes back to Brouwer. Gagliardo and Kottman and later M. Brown have developed topological strategies to locate the fixed point from the position of the cycle. We employ these ideas to study certain classes of homeomorphisms which are useful in the theory of periodic differential equations.
    Mathematics Subject Classification: Primary: 34C25, 37J10; Secondary: 37C25.


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