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| We shall discuss here the bifurcation of small periodic solutions in a time-reversible and conservative four-dimensional nonlinear system that arises in Differential Geometry, in the study of biharmonic maps from torus into spheres. The linearized system has two pairs of pure imaginary eigenvalues, which are double (the case of 1:1 resonance) and non-semisimple. Using a normal form transformation, we reduce the original system to a three-dimensional system, which is analyzed qualitatively with regard to the unfolding parameters. |
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