Aim To study singular points, closed orbits, stable manifolds and unstable manifolds of a second order autonomous Birkhoff system.

In the paper,we have studied the existence of closed orbits for autonomous pla-narsyslem:Some sufficient conditions are established to ensure that the system has at least one closed otbit.

In this paper,we have studied the existence of closed orbits for the generalized Lienard system: x=φ(y), y=-φ(y)f(x)-g(x).

Under the conditions of close orbit an analytical expression resulting in close trajectory is given.

In this paper,the authors studied a mulgimolecules model:(a＞0,p≥1,q≥2)(E)The authors obtained the following result:There exists an a＜a≤ao,such that if a＜(x,y) ∈ G or a＞a_o then(E) has no close orbit；if＜a≤a,then(E)has stable limit cycle.

Shall discuss some geometric properties of homogeneous vector fields of degree three in R 3,especially the geometric structure of the tangent vector field Q T( x ) on the sphere S 2 induced by such vector fields,namely the geometric distribution of singularities,trajectories(including closed orbits,limit cycles)and heteroclinic loops.

In this paper,the authors continue to study the Liapunov bifurcation problem on three dimensional dynamical system on the basis of paper[2],the restrictions on the vector fields are relaxed;the method that judge the existence of periodic solutions generated from the closed orbits is given.

Features and analysis of enclosed track cranes;

 Especially, in the process of closed orbit correction, the electron beam equilibrium orbit is shifted to the center orbit of Hefei storage ring by monitoring the closed orbit distortion due to momentum spread.