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
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
The exponential dichotomy and the theory of transversality are used to give the condition and its geometric significance for the persistence of a singular orbit with higher degeneracy under small autonomous perturbati...The exponential dichotomy and the theory of transversality are used to give the condition and its geometric significance for the persistence of a singular orbit with higher degeneracy under small autonomous perturbations. Examples of the uniquely persisting singular orbits situated on a 2-dimensional cylinder (resp. torus) consisting of heteroclinic (resp. homoclinic) orbits are also given.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.
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].
基金Project supported by the National Natural Science Foundation of China and Shanghai Natural ScienceFoundation.
文摘The exponential dichotomy and the theory of transversality are used to give the condition and its geometric significance for the persistence of a singular orbit with higher degeneracy under small autonomous perturbations. Examples of the uniquely persisting singular orbits situated on a 2-dimensional cylinder (resp. torus) consisting of heteroclinic (resp. homoclinic) orbits are also given.
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.
