97-286 Heinz Han{\ss}mann

The Reversible Umbilic Bifurcation (1266K, PostScript, gzipped and uuencoded) May 20, 97

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Abstract. Hamiltonian systems with several degrees of freedom regularly lead to the investigation of bifurcating equilibria in reduced one-degree-of-freedom systems. This paper concerns equilibria with vanishing linearization, a co-dimension two phenomenon in the reversible context. Under appropriate transversality conditions such equilibria have versal unfoldings related to the elliptic and hyperbolic umbilic catastrophes. This has applications to gyrostat motion and also helps to explain the dynamics defined by the normal form of the H\'enon-Heiles system. The occurring unfoldings turn out to be versal even in the general reversible context of not necessarily Hamiltonian systems.

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