Trivial dynamics for a class of analytic homeomorphisms of the plane

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September 2008, 10(2&3, September): 651-659. doi: 10.3934/dcdsb.2008.10.651

Trivial dynamics for a class of analytic homeomorphisms of the plane

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

Received September 2006 Revised July 2007 Published June 2008

Abstract
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A homeomorphism of the plane $h$ has trivial dynamics if every positive orbit $\{ h^n (p)\}_{n\geq 0}$ is either convergent (to a fixed point) or divergent (to infinity). The main result of this paper says that the property of trivial dynamics can be decided by computing the topological degree of $id -h$. In this result it is assumed that $h$ is analytic in the real sense. Some applications to difference equations and to periodic Newtonian differential equations are obtained.

Keywords: analytic set, periodic solution., degree, Free homeomorphism.

Mathematics Subject Classification: Primary: 37E30; Secondary: 39A11, 34C1.

Citation: Rafael Ortega. Trivial dynamics for a class of analytic homeomorphisms of the plane. Discrete & Continuous Dynamical Systems - B, 2008, 10 (2&3, September) : 651-659. doi: 10.3934/dcdsb.2008.10.651

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