Generalized Hamilton system and gradient system
Abstract
The generalized Hamilton system and the gradient system are two different important dynamical systems. The relation between the two systems is studied. The generalized Hamilton system is a generalization of the Hamilton system. A Birkhoff system can become a generalized Hamilton system under some conditions. The gradient system and its application are given. The relation of the two systems is obtained. Some examples are given to illustrate the application of the result.
