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A study of the Rimmer bifurcation of symmetric fixed points of reversible diffeomorphisms. (English) Zbl 0901.58037
This paper studies the Rimmer bifurcation of symmetric fixed points in two-dimensional discrete reversible dynamical systems. In 1978, Rimmer considered symmetry-breaking bifurcations of a smooth family of area-preserving reversible mappings of the plane. In this paper, the author selects a more convenient generating function than the one used by Rimmer and uses it to show how an analysis of the Rimmer bifurcation can be done either by studying the bifurcation of the critical points of a symmetric Hamiltonian function or by examination of the bifurcation of symmetric equilibrium points for a nonconservative reversible vector field. The author also provides normal forms for generating functions of area-preserving reversible diffeomorphisms as well as normal forms for nonconservative vector fields associated with the Rimmer bifurcation.

MSC:
37G99 Local and nonlocal bifurcation theory for dynamical systems
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