The degenerated homoclinic bifurcation for high dimensional system is considered. The existence, uniqueness, and incoexistence of the 1-homclinic orbit and 1-periodic orbit near Г are studied under the nonresonant c...The degenerated homoclinic bifurcation for high dimensional system is considered. The existence, uniqueness, and incoexistence of the 1-homclinic orbit and 1-periodic orbit near Г are studied under the nonresonant condition. Complicated bifurcation pattern is described under the resonant condition.展开更多
This paper studies the existence of nontrival homoclinic orbits of the Hamiltonian systems -L(t)q+V′(t,q)=0 by using the critical point theory, where the potential V(t,q)=b(t)W(q) can change sign. Under a new kind of...This paper studies the existence of nontrival homoclinic orbits of the Hamiltonian systems -L(t)q+V′(t,q)=0 by using the critical point theory, where the potential V(t,q)=b(t)W(q) can change sign. Under a new kind of "superquadratic" condition on W, some new results are obtained.展开更多
The homoclinic bifurcations in four dimensional vector fields are investigated by setting up a local coordinates near the homoclinic orbit. This homoclinic orbit is nonprincipal in the meanings that its positive semi-...The homoclinic bifurcations in four dimensional vector fields are investigated by setting up a local coordinates near the homoclinic orbit. This homoclinic orbit is nonprincipal in the meanings that its positive semi-orbit takes orbit flip and its unstable foliation takes inclination flip. The existence, nonexistence, uniqueness and coexistence of the 1-homoclinic orbit and the 1-periodic orbit are studied. The existence of the twofold periodic orbit and three-fold periodic orbit are also obtained.展开更多
基金National Natural Science Foundation of China!(No. 19771037)
文摘The degenerated homoclinic bifurcation for high dimensional system is considered. The existence, uniqueness, and incoexistence of the 1-homclinic orbit and 1-periodic orbit near Г are studied under the nonresonant condition. Complicated bifurcation pattern is described under the resonant condition.
文摘This paper studies the existence of nontrival homoclinic orbits of the Hamiltonian systems -L(t)q+V′(t,q)=0 by using the critical point theory, where the potential V(t,q)=b(t)W(q) can change sign. Under a new kind of "superquadratic" condition on W, some new results are obtained.
文摘The homoclinic bifurcations in four dimensional vector fields are investigated by setting up a local coordinates near the homoclinic orbit. This homoclinic orbit is nonprincipal in the meanings that its positive semi-orbit takes orbit flip and its unstable foliation takes inclination flip. The existence, nonexistence, uniqueness and coexistence of the 1-homoclinic orbit and the 1-periodic orbit are studied. The existence of the twofold periodic orbit and three-fold periodic orbit are also obtained.
