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This article is cited in 11 scientific papers (total in 11 papers)
Integrable and non-integrable deformations of the skew Hopf bifurcation
H. W. Broera, F. Takensa, F. O. O. Wagenerb a University of Groningen,
Department of Mathematics,
P.O. Box 800, 9700 AV Groningen, Netherlands
b Mathematics Institute,
University of Warwick,
Coventry CV4 7AL, UK
Abstract:
In the skew Hopf bifurcation a quasi-periodic attractor with nontrivial normal linear dynamics loses hyperbolicity. Periodic, quasi-periodic and chaotic dynamics occur, including motion with mixed spectrum. The case of 3-dimensional skew Hopf bifurcation families of diffeomorphisms near integrability is discussed, surveying some recent results in a broad perspective. One result, using KAM-theory, deals with the persistence of quasi-periodic circles. Other results concern the bifurcations of periodic attractors in the case of resonance.
Received: 29.07.1999
Citation:
H. W. Broer, F. Takens, F. O. O. Wagener, “Integrable and non-integrable deformations of the skew Hopf bifurcation”, Regul. Chaotic Dyn., 4:2 (1999), 16–43
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https://www.mathnet.ru/eng/rcd900 https://www.mathnet.ru/eng/rcd/v4/i2/p16
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Abstract page: | 62 |
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