Using the theory of invariant manifolds, we give local expressions of the stable and unstable manifolds for normally hyperbolic invariant tori, and study the existence of transverse orbits heteroclinic to hyperbolic i...Using the theory of invariant manifolds, we give local expressions of the stable and unstable manifolds for normally hyperbolic invariant tori, and study the existence of transverse orbits heteroclinic to hyperbolic invariant tori. These extend and improve the corresponding results obtained in [3-5].展开更多
It is proved for parabolic equations that under certain conditions the weak (un-) stable manifolds possess invariant foliations, called strongly (un-) stable foliations. The relevant results on center manifoids are ge...It is proved for parabolic equations that under certain conditions the weak (un-) stable manifolds possess invariant foliations, called strongly (un-) stable foliations. The relevant results on center manifoids are generalized to weak hyperbolic manifolds展开更多
A geometrical method using the exponential dichotomy and the invariant manifold thoery is given to set up the criteria for the existence of transversal and tangential heterodinic orbits under the most general degenera...A geometrical method using the exponential dichotomy and the invariant manifold thoery is given to set up the criteria for the existence of transversal and tangential heterodinic orbits under the most general degenerate cases. Conclusions given here extend and contain the relevant known results.展开更多
A generalized method combining the exponential dichotomy and the theory of transversality was used to give conditions for the persistence and transversality of homoclinic orbits under small perturbation for the diffeo...A generalized method combining the exponential dichotomy and the theory of transversality was used to give conditions for the persistence and transversality of homoclinic orbits under small perturbation for the diffeomorphisms.展开更多
By using the geometrical method, the higher order Melnikov vector and the associatedcriteria for the persistence, transversality and tangency of homoclinic and heteroclinic orbits are established. Examples of applicat...By using the geometrical method, the higher order Melnikov vector and the associatedcriteria for the persistence, transversality and tangency of homoclinic and heteroclinic orbits are established. Examples of application are also given.展开更多
基金Supported by the National Natural Science Foundation of China Shanghai Natural Science Foundation.
文摘Using the theory of invariant manifolds, we give local expressions of the stable and unstable manifolds for normally hyperbolic invariant tori, and study the existence of transverse orbits heteroclinic to hyperbolic invariant tori. These extend and improve the corresponding results obtained in [3-5].
文摘It is proved for parabolic equations that under certain conditions the weak (un-) stable manifolds possess invariant foliations, called strongly (un-) stable foliations. The relevant results on center manifoids are generalized to weak hyperbolic manifolds
基金Project supported by the National Natural Science Foundation of China.
文摘A geometrical method using the exponential dichotomy and the invariant manifold thoery is given to set up the criteria for the existence of transversal and tangential heterodinic orbits under the most general degenerate cases. Conclusions given here extend and contain the relevant known results.
文摘A generalized method combining the exponential dichotomy and the theory of transversality was used to give conditions for the persistence and transversality of homoclinic orbits under small perturbation for the diffeomorphisms.
文摘By using the geometrical method, the higher order Melnikov vector and the associatedcriteria for the persistence, transversality and tangency of homoclinic and heteroclinic orbits are established. Examples of application are also given.
