American Institute of Mathematical Sciences

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May  2008, 9(3&4, May): 517-523. doi: 10.3934/dcdsb.2008.9.517

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, Spain
2. 

Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, 18071 Granada

Received  January 2007 Revised  May 2007 Published  February 2008

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.
Keywords: Two cycle, subharmonic solution, forced oscillator..
Mathematics Subject Classification: Primary: 34C25, 37J10; Secondary: 37C2.
Citation: Juan Campos, Rafael Ortega. Location of fixed points and periodic solutions in the plane. Discrete & Continuous Dynamical Systems - B, 2008, 9 (3&4, May) : 517-523. doi: 10.3934/dcdsb.2008.9.517
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