The Maslov P-index theory for a symplectic path is defined. Various properties of this index theory such as homotopy invariant, symplectic additivity and the relations with other Morse indices are studied. As an appli...The Maslov P-index theory for a symplectic path is defined. Various properties of this index theory such as homotopy invariant, symplectic additivity and the relations with other Morse indices are studied. As an application, the non-periodic problem for some asymptotically linear Hamiltonian systems is considered.展开更多
Let P C Sp（2n） satisfying pk = I2n. We consider the minimal P-symmetric period problem of the autonomous nonlinear Hamiltonian system x（t） = JH＇（x（t））. For some symplectic matrices P, we show that for any π...Let P C Sp（2n） satisfying pk = I2n. We consider the minimal P-symmetric period problem of the autonomous nonlinear Hamiltonian system x（t） = JH＇（x（t））. For some symplectic matrices P, we show that for any π 〉0,the above Hamiltonian system possesses a kT periodic solution x with kT being its minimal P-symmetric period provided H satisfies Rabinowitz＇s conditions on the minimal period conjecture, together with that H is convex and H（Px） = H（x）.展开更多
基金Project supported by the National Natural Science Foundation of China (No.10531050) and FANEDD.
文摘The Maslov P-index theory for a symplectic path is defined. Various properties of this index theory such as homotopy invariant, symplectic additivity and the relations with other Morse indices are studied. As an application, the non-periodic problem for some asymptotically linear Hamiltonian systems is considered.
基金This work was partially supported by the National Natural Science Foundation of China （Grant No. 11471170）.
文摘Let P C Sp（2n） satisfying pk = I2n. We consider the minimal P-symmetric period problem of the autonomous nonlinear Hamiltonian system x（t） = JH＇（x（t））. For some symplectic matrices P, we show that for any π 〉0,the above Hamiltonian system possesses a kT periodic solution x with kT being its minimal P-symmetric period provided H satisfies Rabinowitz＇s conditions on the minimal period conjecture, together with that H is convex and H（Px） = H（x）.
