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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

Rafael Ortega 1,

1. 

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

Received  September 2006 Revised  July 2007 Published  June 2008

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 and Continuous Dynamical Systems - B, 2008, 10 (2&3, September) : 651-659. doi: 10.3934/dcdsb.2008.10.651
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