Abstract
Consider a Hamiltonian system of two degrees of freedom at an equilibrium. Suppose that the linearized vectorfield has eigenvaluesiα,iα,−iα,−iα (α ∈ ℝ, α>0) and is not semisimple. In this paper we discuss the real normalization of the Hamiltonian function of such a system. We normalize the Hamiltonian up to 4th order and show how to compute its coefficients. For the planar restricted three body problem atL 4 the coefficient that plays an important role in the investigation of the qualitative behaviour of periodic solutions near the equilibrium is explicitly calculated.
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Van Der Meer, JC. Nonsemisimple 1∶1 resonance at an equilibrium. Celestial Mechanics 27, 131–149 (1982). https://doi.org/10.1007/BF01271688
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DOI: https://doi.org/10.1007/BF01271688