Abstract
Without parameters, no periodic orbits bifurcate. Depending on the drift condition, two cases appear. Both are discussed in this chapter.
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References
Fiedler, B., Liebscher, S., Alexander, J.: Generic Hopf bifurcation from lines of equilibria without parameters: I. Theory. J. Differ. Equat. 167, 16–35 (2000)
Fiedler, B., Scheurle, J.: Discretization of Homoclinic Orbits and Invisible Chaos, Mem. AMS, vol. 570. Amer. Math. Soc., Providence (1996)
Gelfreich, V.: A proof of the exponentially small transversality of the separatrices for the standard map. Commun. Math. Phys. 201, 155–216 (1999)
Marsden, J.E., McCracken, M.: The Hopf bifurcartion and its applications. Appl. Math. Sci., vol. 19. Springer, New York (1976)
Neishtadt, A.: On the separation of motions in systems with rapidly rotating phase. J. Appl. Math. Mech. 48, 134–139 (1984)
Vanderbauwhede, A.: Centre manifolds, normal forms and elementary bifurcations. In: Kirchgraber, U., Walther, H.O. (eds.) Dynamics Reported 2, pp. 89–169. Teubner & Wiley, Stuttgart (1989)
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Liebscher, S. (2015). Poincaré-Andronov-Hopf Bifurcation. In: Bifurcation without Parameters. Lecture Notes in Mathematics, vol 2117. Springer, Cham. https://doi.org/10.1007/978-3-319-10777-6_5
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DOI: https://doi.org/10.1007/978-3-319-10777-6_5
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