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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 of multi-bump homoclinics in systems with normal and slow variables.

Fečkan, Michal (2000)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Bifurcations of limit cycles from cubic Hamiltonian systems with a center and a homoclinic saddle-loop.

Yulin Zhao, Zhifen Zhang (2000)

Publicacions Matemàtiques

It is proved in this paper that the maximum number of limit cycles of system⎧ dx/dt = y⎨⎩ dy/dt = kx - (k + 1)x2 + x3 + ε(α + βx + γx2)yis equal to two in the finite plane, where k > (11 + √33) / 4 , 0 < |ε| << 1, |α| + |β| + |γ| ≠ 0. This is partial answer to the seventh question in [2], posed by Arnold.

Displaying 1 – 3 of 3

Bifurcation of heteroclinic orbits for diffeomorphisms

Bifurcation of multi-bump homoclinics in systems with normal and slow variables.

Bifurcations of limit cycles from cubic Hamiltonian systems with a center and a homoclinic saddle-loop.

Currently displaying 1 – 3 of 3