Unfolding of nilpotent equilibria of degree 4 in Hamiltonian systems with 2 degrees of freedom

Giannis Moutsinas

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arXiv · 1706.08185

Unfolding of nilpotent equilibria of degree 4 in Hamiltonian systems with 2 degrees of freedom

Giannis Moutsinas

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Abstract

We consider Hamiltonian systems of two degrees of freedome having a nilpotent equilibrium point with only one eigenvector. We provide the universal unfolding of such equilibrium, provided a non-degeneracy condition holds. We show that the only co-dimension 1 bifurcations that happen in the unfolding are of two types: the normally hyperbolic or elliptic centre-saddle bifurcations and the supercritical Hamiltonian-Hopf bifurcation.

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Giannis Moutsinas. 2017-06-25. Unfolding of nilpotent equilibria of degree 4 in Hamiltonian systems with 2 degrees of freedom. https://arxiv.org/abs/1706.08185

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