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Bifurcation of heteroclinic orbits for diffeomorphisms

Michal Fečkan (1991)

Applications of Mathematics

The paper deals with the bifurcation phenomena of heteroclinic orbits for diffeomorphisms. The existence of a Melnikov-like function for the two-dimensional case is shown. Simple possibilities of the set of heteroclinic points are described for higherdimensional cases.

Bifurcation set and limit cycles forming compound eyes in a perturbed Hamiltonian system.

Li Jibin, Liu Zhenrong (1991)

Publicacions Matemàtiques

In this paper we consider a class of perturbation of a Hamiltonian cubic system with 9 finite critical points. Using detection functions, we present explicit formulas for the global and local bifurcations of the flow. We exhibit various patterns of compound eyes of limit cycles. These results are concerned with the weakened Hilbert's 16th problem posed by V. I. Arnold in 1977.

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