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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

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.
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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