Geodesic
The Andronov--Hopf bifurcation with~$2:1$ resonance
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems. Part VIII, Tome 300 (2003), pp. 259-265

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We consider dissipative dynamical systems in the neighborhood of quasi-periodic $n$-dimensional invariant tori that are not normally hyperbolic. We assume that the normal spectrum contains precisely two pairs of simple pure imaginary eigenvalues. We investigate the case where the frequencies are in the ratio $2:1$. We establish sufficient conditions for the existence of invariant tori of dimension $n+p$ in certain region of the parameter space. 
@article{ZNSL_2003_300_a26,
     author = {D. Yu. Volkov},
     title = {The {Andronov--Hopf} bifurcation with~$2:1$ resonance},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {259--265},
     publisher = {mathdoc},
     volume = {300},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_300_a26/}
}
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D. Yu. Volkov. The Andronov--Hopf bifurcation with~$2:1$ resonance. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems. Part VIII, Tome 300 (2003), pp. 259-265. http://geodesic.mathdoc.fr/item/ZNSL_2003_300_a26/