Using the technique of the Lyapunov direct method and the dissipative structural properties of Hamiltonian systems,some sufficient conditions are derived for the stability of several classes of time-delay Hamiltonian systems.

Hopf bifurcation based on a three-dimensional and time-dependent perturbation Hamiltonian system;

Some results of discrete Hamiltonian systems;

The same distribution of limit cycles in nine perturbed Hamiltonian systems;

Hamiltonian systems modeling and control of a doubly-fed induction machine;

The existence of the periodic solutions for a class of superquadratic autonomous Hamiltonian systems is proved by using the linking theorem combining with the Maslov index theory.

A generalized KAM theorem for lower dimensional tori in Hamiltonian systems is obtained, which applies to the case where there are normal frequencies and hyperbolic normal components simultaneously.

The paper draws the locus on the Poincare cross section under different energies in Hamilton system by using tetrava- lent Romberg-Coota method with regular motion equations,indicating that the change occurs in the system from stability to disorder within a small energy range.

A lattice Boltzamnn model for the Hamilton system is given.