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2013
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# Florian Wagener

 Broer H. W., Takens F., Wagener F. O. Integrable and non-integrable deformations of the skew Hopf bifurcation 1999, vol. 4, no. 2, pp.  17-43 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. Citation: Broer H. W., Takens F., Wagener F. O.,  Integrable and non-integrable deformations of the skew Hopf bifurcation, Regular and Chaotic Dynamics, 1999, vol. 4, no. 2, pp. 17-43 DOI:10.1070/RD1999v004n02ABEH000103