Geodesic
On the Pseudonormal Form of Real Autonomous Systems with Two Pure Imaginary Eigenvalues
Matematičeskie zametki, Tome 92 (2012) no. 5, pp. 731-746

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The paper deals with real autonomous systems of ordinary differential equations in a neighborhood of a nondegenerate singular point such that the matrix of the linearized system has two pure imaginary eigenvalues, all other eigenvalues lying outside the imaginary axis. The reducibility of such systems to pseudonormal form is studied. The notion of resonance is refined, and the notions of removable and irremovable resonances are introduced.
Keywords: ordinary differential equations, linearization, normal form, pseudonormal form, resonance. 
@article{MZM_2012_92_5_a8,
     author = {V. S. Samovol},
     title = {On the {Pseudonormal} {Form} of {Real} {Autonomous} {Systems} with {Two} {Pure} {Imaginary} {Eigenvalues}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {731--746},
     publisher = {mathdoc},
     volume = {92},
     number = {5},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_92_5_a8/}
}
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V. S. Samovol. On the Pseudonormal Form of Real Autonomous Systems with Two Pure Imaginary Eigenvalues. Matematičeskie zametki, Tome 92 (2012) no. 5, pp. 731-746. http://geodesic.mathdoc.fr/item/MZM_2012_92_5_a8/