A concrete numerical example of Z6-equivariant planar perturbed Hamiltonian polynomial vector fields of degree 5 having at least 24 limit cycles and the configurations of compound eyes are given by using the bifurcati...A concrete numerical example of Z6-equivariant planar perturbed Hamiltonian polynomial vector fields of degree 5 having at least 24 limit cycles and the configurations of compound eyes are given by using the bifurcation theory of planar dynamical systems and the method of detection functions. There is reason to conjecture that the Hilbert number H(2k + 1) ? (2k + I)2 - 1 for the perturbed Hamiltonian systems.展开更多
For the real planar autonomous differential system, the questionsof detection between center and focus, successor function, formal series, central integration, integration factor, focal values, values of singular poin...For the real planar autonomous differential system, the questionsof detection between center and focus, successor function, formal series, central integration, integration factor, focal values, values of singular point and bifurcation of limit cycles for a class of higher-degree critical points and infinite points are expounded.展开更多
Let L be a double homoclinic loop of a Hamiltonian system on the plane. We obtain a condition under which L generates at most two large limit cycles by perturbations. We also give conditions for the existence of at mo...Let L be a double homoclinic loop of a Hamiltonian system on the plane. We obtain a condition under which L generates at most two large limit cycles by perturbations. We also give conditions for the existence of at most five or six limit cycles which appear near L under perturbations.展开更多
基金This work was supported by the Strategic Research (Grant No. 7000934) from the City University of Hong Kong.
文摘A concrete numerical example of Z6-equivariant planar perturbed Hamiltonian polynomial vector fields of degree 5 having at least 24 limit cycles and the configurations of compound eyes are given by using the bifurcation theory of planar dynamical systems and the method of detection functions. There is reason to conjecture that the Hilbert number H(2k + 1) ? (2k + I)2 - 1 for the perturbed Hamiltonian systems.
基金This work was supported by the Natural Science Foundation of Hunan Province (Grant No. 10071016) .
文摘For the real planar autonomous differential system, the questionsof detection between center and focus, successor function, formal series, central integration, integration factor, focal values, values of singular point and bifurcation of limit cycles for a class of higher-degree critical points and infinite points are expounded.
文摘Let L be a double homoclinic loop of a Hamiltonian system on the plane. We obtain a condition under which L generates at most two large limit cycles by perturbations. We also give conditions for the existence of at most five or six limit cycles which appear near L under perturbations.
