In this paper, the conservation laws of generalized Birkhoff system in event space are studied by using the method of integrating factors. Firstly, the generalized Pfaff-Birkhoff principle and the generalized Birkhoff...In this paper, the conservation laws of generalized Birkhoff system in event space are studied by using the method of integrating factors. Firstly, the generalized Pfaff-Birkhoff principle and the generalized Birkhoff equations are established, and the definition of the integrating factors for the system is given. Secondly, based on the concept of integrating factors, the conservation theorems and their inverse for the generalized Birkhoff system in the event space are presented in detail, and the relation between the conservation laws and the integrating factors of the system is obtained and the generalized Killing equations for the determination of the integrating factors are given. Finally, an example is given to illustrate the application of the results.展开更多
The combined gradient representations for generalized Birkhoffian systems in event space are studied.Firstly,the definitions of six kinds of combined gradient systems and corresponding differential equations are given...The combined gradient representations for generalized Birkhoffian systems in event space are studied.Firstly,the definitions of six kinds of combined gradient systems and corresponding differential equations are given.Secondly,the conditions under which generalized Birkhoffian systems become combined gradient systems are obtained. Finally,the characteristics of combined gradient systems are used to study the stability of generalized Birkhoffian systems in event space. Seven examples are given to illustrate the results.展开更多
基金supported by National Natural Science Foundation of China under Grant No. 10572021
文摘In this paper, the conservation laws of generalized Birkhoff system in event space are studied by using the method of integrating factors. Firstly, the generalized Pfaff-Birkhoff principle and the generalized Birkhoff equations are established, and the definition of the integrating factors for the system is given. Secondly, based on the concept of integrating factors, the conservation theorems and their inverse for the generalized Birkhoff system in the event space are presented in detail, and the relation between the conservation laws and the integrating factors of the system is obtained and the generalized Killing equations for the determination of the integrating factors are given. Finally, an example is given to illustrate the application of the results.
基金supported by the National Natural Science Foundation of China(No.11972241)the Natural Science Foundation of Jiangsu Province (No.BK20191454)the Scientific Research Foundation of Suzhou University of Science and Technology (No.XKZ2017005)。
文摘The combined gradient representations for generalized Birkhoffian systems in event space are studied.Firstly,the definitions of six kinds of combined gradient systems and corresponding differential equations are given.Secondly,the conditions under which generalized Birkhoffian systems become combined gradient systems are obtained. Finally,the characteristics of combined gradient systems are used to study the stability of generalized Birkhoffian systems in event space. Seven examples are given to illustrate the results.
