Geodesic
Local Finitely Smooth Equivalence of Real Autonomous Systems with Two Pure Imaginary Eigenvalues
Matematičeskie zametki, Tome 92 (2012) no. 6, pp. 912-927

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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. It is proved that, for such systems having a focus on the center manifold, the problem of finitely smooth equivalence is solved in terms of the finite segments of the Taylor series of their right-hand sides.
Keywords: autonomous system of ordinary differential equations, finitely smooth equivalence of systems, pseudonormal form, resonance, shearing transformation. 
@article{MZM_2012_92_6_a11,
     author = {V. S. Samovol},
     title = {Local {Finitely} {Smooth} {Equivalence} of {Real} {Autonomous} {Systems} with {Two} {Pure} {Imaginary} {Eigenvalues}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {912--927},
     publisher = {mathdoc},
     volume = {92},
     number = {6},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_92_6_a11/}
}
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V. S. Samovol. Local Finitely Smooth Equivalence of Real Autonomous Systems with Two Pure Imaginary Eigenvalues. Matematičeskie zametki, Tome 92 (2012) no. 6, pp. 912-927. http://geodesic.mathdoc.fr/item/MZM_2012_92_6_a11/