Abstract
In this chapter we discuss bifurcations from equilibria which have multiple degeneracies. We start with the analogues of the sadble-node and Hopf bifurcations with the same linear part, but additional degeneracy in the nonlinear terms of the Taylor expansion expressed in normal form. The theory here is complete, at least for the first few cases, and is essentially obtained by unfolding degenerate singularities of functions, since in each case we can reduce to a noe-dimensional flow.
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© 1983 Springer Science+Business Media New York
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Guckenheimer, J., Holmes, P. (1983). Local Codimension Two Bifurcations of Flows. In: Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences, vol 42. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1140-2_7
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DOI: https://doi.org/10.1007/978-1-4612-1140-2_7
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-7020-1
Online ISBN: 978-1-4612-1140-2
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