Poisson theory and integration method of Birkhoffian systems in the event space

doi:10.1088/1674-1056/19/8/080301

中国物理B ›› 2010, Vol. 19 ›› Issue (8): 80301-080301.doi: 10.1088/1674-1056/19/8/080301

Poisson theory and integration method of Birkhoffian systems in the event space

张毅

College of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, China

收稿日期:2010-03-17 修回日期:2010-03-22 出版日期:2010-08-15 发布日期:2010-08-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 10972151).

Poisson theory and integration method of Birkhoffian systems in the event space

Zhang Yi(张毅)^†

College of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, China

Received:2010-03-17 Revised:2010-03-22 Online:2010-08-15 Published:2010-08-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 10972151).

摘要/Abstract

摘要： This paper focuses on studying the Poisson theory and the integration method of a Birkhoffian system in the event space. The Birkhoff's equations in the event space are given. The Poisson theory of the Birkhoffian system in the event space is established. The definition of the Jacobi last multiplier of the system is given, and the relation between the Jacobi last multiplier and the first integrals of the system is discussed. The researches show that for a Birkhoffian system in the event space, whose configuration is determined by (2n+1) Birkhoff's variables, the solution of the system can be found by the Jacobi last multiplier if 2n first integrals are known. An example is given to illustrate the application of the results.

Abstract: This paper focuses on studying the Poisson theory and the integration method of a Birkhoffian system in the event space. The Birkhoff's equations in the event space are given. The Poisson theory of the Birkhoffian system in the event space is established. The definition of the Jacobi last multiplier of the system is given, and the relation between the Jacobi last multiplier and the first integrals of the system is discussed. The researches show that for a Birkhoffian system in the event space, whose configuration is determined by (2n+1) Birkhoff's variables, the solution of the system can be found by the Jacobi last multiplier if 2n first integrals are known. An example is given to illustrate the application of the results.

Key words: Birkhoffian system, event space, method of integration, Jacobi last multiplier

中图分类号: (Measure and integration)

02.30.Cj

02.30.Jr (Partial differential equations) 02.50.Ey (Stochastic processes)

张毅. Poisson theory and integration method of Birkhoffian systems in the event space[J]. 中国物理B, 2010, 19(8): 80301-080301.

Zhang Yi(张毅). Poisson theory and integration method of Birkhoffian systems in the event space[J]. Chin. Phys. B, 2010, 19(8): 80301-080301.

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Poisson theory and integration method of Birkhoffian systems in the event space

Poisson theory and integration method of Birkhoffian systems in the event space

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