自治Birkhoff系统的四类梯度表示（英文）

Four kinds of gradient representations of autonomous Birkhoffian systems

提出四类梯度系统,并研究自治Birkhoff系统的梯度表示.给出系统成为梯度表示和分数维梯度的条件,利用梯度系统的性质来研究Birkhoff系统的积分和解的稳定性,举例说明结果的应用.

In order to study the integration and the stability of autonomous Birkhoffian systems, we propose four klnds of gradient systems to represent the autonomous Birkhoffian systems. By analysing the relationship between the gradient systems and the Birkhoffian systems, we obtain the conditions that the Birkhoffian systems can be transformed into a kind of four gradient systems. Then, we use the properties of gradient system to investigate the problems of integration and stability of the Birkhoffian systems. Finally, we give some examples to illustrate the application of the theory.