Science in China Series A-Mathematics Physics Astronomy & Technological Science · 1990 · 158 citations · 0 references
Natural SciencesMathematicsComplex SystemsDifferential EquationsDynamical SystemsGroup TheoryHamiltonian DynamicsHamiltonian MechanicsHamiltonian SystemsLie GroupsSymplectic GeometryCritical PointsDegenerate Critical PointsIndex TheoryMaslov IndexNondegenerate Critical PointsPeriodic Orbits In Hamiltonian SystemsPeriodic Solutions Of Differential EquationsSymplectic Forms
This paper introduces a Maslov-type index theory for paths in the symplectic groups, especially for the degenerate paths via rotational perturbation method, therefore gives a full classification of the linear Hamiltonian systems with continuous, periodic, and symmetric coefficients. Associating this index with each periodic solution, we establish the existence of muhiple periodic solutions of asymptotically linear Hamihonian systems.