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

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

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.

Keywords: Birkhoffian system event space method of integration Jacobi last multiplier

Received: 17 March 2010
Revised: 22 March 2010
Accepted manuscript online:

PACS:	02.30.Cj	(Measure and integration)
	02.30.Jr	(Partial differential equations)
	02.50.Ey	(Stochastic processes)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 10972151).

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Zhang Yi(张毅) Poisson theory and integration method of Birkhoffian systems in the event space 2010 Chin. Phys. B 19 080301

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