Resonance and bifurcation of higher-dimensional tori

Flockerzi, Dietrich

doi:10.1090/S0002-9939-1985-0781073-5

Resonance and bifurcation of higher-dimensional tori
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Proc. Amer. Math. Soc. 94 (1985), 147-157 Request permission

Abstract:

By means of an example it is shown that a supercritical bifurcation of an invariant $2$-torus into an invariant $3$-torus prevailing in the case of nonresonance may be replaced by a transcritical bifurcation into a pinched invariant $3$-torus in the case of resonance. The connections of these bifurcation phenomena with the properties of the spectrum of the underlying invariant $2$-torus are discussed.

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