Ⅰ. INTRODUCTION The famous Comet Halley (whose period P=76.1 years, orbital eccentricity e=0.9673, inclination of orbit i=16202) threw men into a great panic and nervous state on May 18, 1910 before its flying past t...Ⅰ. INTRODUCTION The famous Comet Halley (whose period P=76.1 years, orbital eccentricity e=0.9673, inclination of orbit i=16202) threw men into a great panic and nervous state on May 18, 1910 before its flying past the earth. When the comet’s tail swept over展开更多
Homoclinic bifurcations in four-dimensional vector fields are investigated by setting up a local coordinate near a homoclinic orbit. This homoclinic orbit is principal but its stable and unstable foliations take incli...Homoclinic bifurcations in four-dimensional vector fields are investigated by setting up a local coordinate near a homoclinic orbit. This homoclinic orbit is principal but its stable and unstable foliations take inclination flip. The existence, nonexistence, and uniqueness of the 1-homoclinic orbit and 1-periodic orbit are studied. The existence of the two-fold 1-periodic orbit and three-fold 1 -periodic orbit are also obtained. It is indicated that the number of periodic orbits bifurcated from this kind of homoclinic orbits depends heavily on the strength of the inclination flip.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
One orbit flip and two inclination flips bifurcation is considered with resonant principal eigenvalues. We introduce a local active coordinate system to establish bifurcation equation and obtain the conditions when th...One orbit flip and two inclination flips bifurcation is considered with resonant principal eigenvalues. We introduce a local active coordinate system to establish bifurcation equation and obtain the conditions when the original homoclinic orbit is kept or broken. We also prove the existence and the existence regions of double 1-periodic orbit bifurcation. Moreover, the complicated homoclinic-doubling bifurcations are found and expressed approximately, and are well located.展开更多
文摘Ⅰ. INTRODUCTION The famous Comet Halley (whose period P=76.1 years, orbital eccentricity e=0.9673, inclination of orbit i=16202) threw men into a great panic and nervous state on May 18, 1910 before its flying past the earth. When the comet’s tail swept over
基金This paper was completed when the first author was visiting East China Normal University.This work was supported by the National Natural Science Foundation of China(Grant No.10071022).
文摘Homoclinic bifurcations in four-dimensional vector fields are investigated by setting up a local coordinate near a homoclinic orbit. This homoclinic orbit is principal but its stable and unstable foliations take inclination flip. The existence, nonexistence, and uniqueness of the 1-homoclinic orbit and 1-periodic orbit are studied. The existence of the two-fold 1-periodic orbit and three-fold 1 -periodic orbit are also obtained. It is indicated that the number of periodic orbits bifurcated from this kind of homoclinic orbits depends heavily on the strength of the inclination flip.
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.
文摘One orbit flip and two inclination flips bifurcation is considered with resonant principal eigenvalues. We introduce a local active coordinate system to establish bifurcation equation and obtain the conditions when the original homoclinic orbit is kept or broken. We also prove the existence and the existence regions of double 1-periodic orbit bifurcation. Moreover, the complicated homoclinic-doubling bifurcations are found and expressed approximately, and are well located.
