Location of fixed points and periodic solutions in the plane

Juan Campos; Rafael Ortega

doi:10.3934/dcdsb.2008.9.517

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2008, Volume 9, Issue 3&4: 517-523. Doi: 10.3934/dcdsb.2008.9.517

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Location of fixed points and periodic solutions in the plane

Juan Campos^1, and
Rafael Ortega^2,

1.
Departamento de Matemática Aplicada, Universidad de Granada, 18071 Granada
2.
Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, 18071 Granada

Received: January 2007

Revised: May 2007

Published: May 2008

Abstract / Introduction Related Papers Cited by

Abstract

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.

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Mathematics Subject Classification: Primary: 34C25, 37J10; Secondary: 37C25.

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