Symplectic Structure of Discrete Hamiltonian Systems

Author： Shi Y.  

Publisher： Academic Press

ISSN： 0022-247X

Source： Journal of Mathematical Analysis and Applications, Vol.266, Iss.2, 2002-02, pp. : 472-478

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Abstract

This paper is concerned with the symplectic structure of discrete nonlinear Hamiltonian systems. The results are related to an open problem that was first proposed by C. D. Ahlbrandt [J. Math. Anal. Appl. 180 (1993), 498–517] discussed elsewhere in the literature. But we give a different statement and different proof. Under a solvable condition, we show that the solution operator of a discrete nonlinear Halmiltonian system is symplectic. Then its phase flow is a discrete one-parameter family of symplectic transformations and preserves the phase volume. © 2002 Elsevier Science (USA).

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