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Symplectic Structure of Discrete Hamiltonian Systems

✍ Scribed by Yuming Shi

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
68 KB
Volume
266
Category
Article
ISSN
0022-247X

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✦ Synopsis

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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