Geodesic
Conservation and bifurcation of an invariant torus of a vector field
Matematičeskie zametki, Tome 61 (1997) no. 1, pp. 34-44 
Yu. N. Bibikov. Conservation and bifurcation of an invariant torus of a vector field. Matematičeskie zametki, Tome 61 (1997) no. 1, pp. 34-44. http://geodesic.mathdoc.fr/item/MZM_1997_61_1_a4/
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     title = {Conservation and bifurcation of an invariant torus of a~vector field},
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     url = {http://geodesic.mathdoc.fr/item/MZM_1997_61_1_a4/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We consider small perturbations with respect to a small parameter $\varepsilon\ge0$ of a smooth vector field in $\mathbb R^{n+m}$ possessing an invariant torus $T_m$. The flow on the torus $T_m$ is assumed to be quasiperiodic with $m$ basic frequencies satisfying certain conditions of Diophantine type; the matrix $\Omega$ of the variational equation with respect to the invariant torus is assumed to be constant. We investigate the existence problem for invariant tori of different dimensions for the case in which $\Omega$ is a nonsingular matrix that can have purely imaginary eigenvalues.

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