Geodesic
Bifurcation of Invariant Tori of Codimension One
Matematičeskie zametki, Tome 69 (2001) no. 1, pp. 3-17.

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We propose a method for constructing classes of real systems of differential equations of order $2^d$ ($d\ge1$), including polynomial systems, in which for all sufficiently small positive values of the parameter a bifurcation from the point of equilibrium to invariant tori of dimension $2^d-1$ occurs. 
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     title = {Bifurcation of {Invariant} {Tori} of {Codimension} {One}},
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V. V. Basov. Bifurcation of Invariant Tori of Codimension One. Matematičeskie zametki, Tome 69 (2001) no. 1, pp. 3-17. http://geodesic.mathdoc.fr/item/MZM_2001_69_1_a0/

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[2] Hale J. K., “Integral manifolds of perturbed differential systems”, Ann. of Math., 73:3 (1961), 496–531 | DOI | MR | Zbl

[3] Maffei C., Negrini P., Scalla M., “Bifurcation from 2-dimensional to $3$-dimensional invariant tori”, Ann. di Matematica pura ed applicata (IV), CLV (1989), 117–136 | DOI | MR