Aim To study singular points, closed orbits, stable manifolds and unstable manifolds of a second order autonomous Birkhoff system. Methods Qualitative methods of ordinary differential equation were used. Results and ...Aim To study singular points, closed orbits, stable manifolds and unstable manifolds of a second order autonomous Birkhoff system. Methods Qualitative methods of ordinary differential equation were used. Results and Conclusion The criteria for singular points, closed orbits and hyperbolic equilibrium points of a second order autonomous Birkhoff system are given. Moreover the stability of equilibria, stable manifolds and unstable manifolds are obtained.展开更多
In this paper we consider the extreme points of closed convex hull of the class T σ(p,α) and then it is used to determine the coefficient bounds. Some other interesting properties of the class T σ(p,α) are also...In this paper we consider the extreme points of closed convex hull of the class T σ(p,α) and then it is used to determine the coefficient bounds. Some other interesting properties of the class T σ(p,α) are also investigated.展开更多
文摘Aim To study singular points, closed orbits, stable manifolds and unstable manifolds of a second order autonomous Birkhoff system. Methods Qualitative methods of ordinary differential equation were used. Results and Conclusion The criteria for singular points, closed orbits and hyperbolic equilibrium points of a second order autonomous Birkhoff system are given. Moreover the stability of equilibria, stable manifolds and unstable manifolds are obtained.
文摘In this paper we consider the extreme points of closed convex hull of the class T σ(p,α) and then it is used to determine the coefficient bounds. Some other interesting properties of the class T σ(p,α) are also investigated.