This paper deals with a class of quadratic Hamiltonian systems with quadratic perturbation. The authors prove that if the first order Melnikov function M1 (h) 0 and the second order Melnikov function M2(h) 0, then...This paper deals with a class of quadratic Hamiltonian systems with quadratic perturbation. The authors prove that if the first order Melnikov function M1 (h) 0 and the second order Melnikov function M2(h) 0, then the origin of the Hamiltonian system with small perturbation is a center.展开更多
An analytical method for predicting chaos in perturbed planar non Hamiltonian integrable systems with slowly varying parameters was developed. Based on the analysis of the geometric structure of unperturbed systems, ...An analytical method for predicting chaos in perturbed planar non Hamiltonian integrable systems with slowly varying parameters was developed. Based on the analysis of the geometric structure of unperturbed systems, the condition of transversely homoclinic intersection was given. The generalized Melnikov function of the perturbed system was found by applying the theorem on the differentiability of ordinary differential equation solutions with respect to parameters.展开更多
This paper studies the number of limit cycles of some Z3-equivariant near-Hamiltonian systems of degrees 3 and 4,which are a perturbation of a cubic Hamiltonian system. By the Melnikov function method,we obtain 5 and ...This paper studies the number of limit cycles of some Z3-equivariant near-Hamiltonian systems of degrees 3 and 4,which are a perturbation of a cubic Hamiltonian system. By the Melnikov function method,we obtain 5 and 6 limit cycles respectively.展开更多
基金This work is supported by NNSF of China (19531070)
文摘This paper deals with a class of quadratic Hamiltonian systems with quadratic perturbation. The authors prove that if the first order Melnikov function M1 (h) 0 and the second order Melnikov function M2(h) 0, then the origin of the Hamiltonian system with small perturbation is a center.
文摘An analytical method for predicting chaos in perturbed planar non Hamiltonian integrable systems with slowly varying parameters was developed. Based on the analysis of the geometric structure of unperturbed systems, the condition of transversely homoclinic intersection was given. The generalized Melnikov function of the perturbed system was found by applying the theorem on the differentiability of ordinary differential equation solutions with respect to parameters.
基金supported by Leading Academic Discipline Project of Shanghai Normal University (DZL707)the National Ministry of Education of China (20060270001)Shanghai Leading Academic Discipline Project (S30405)
文摘This paper studies the number of limit cycles of some Z3-equivariant near-Hamiltonian systems of degrees 3 and 4,which are a perturbation of a cubic Hamiltonian system. By the Melnikov function method,we obtain 5 and 6 limit cycles respectively.
基金the Natural Science Foundation of Anhui Province(1308085MA08)the Doctor Program Foundation(2012)of Anhui Normal University+1 种基金the NNSF of China(11271197)the key NSF of Education Ministry of China(207047)
