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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Resonance and bifurcation of higher-dimensional tori


Author: Dietrich Flockerzi
Journal: Proc. Amer. Math. Soc. 94 (1985), 147-157
MSC: Primary 58F14; Secondary 34C45
MathSciNet review: 781073
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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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DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0781073-5
PII: S 0002-9939(1985)0781073-5
Article copyright: © Copyright 1985 American Mathematical Society