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Symplectic completion of symplectic jets

Rangarajan, Govindan (1996) Symplectic completion of symplectic jets. In: Journal of Mathematical Physics, 37 (9). pp. 4514-4542.

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Abstract

In this paper, we outline a method for symplectic integration of three degree-of-freedom Hamiltonian systems. We start by representing the Hamiltonian system as a symplectic map. This map (in general) has an infinite Taylor series. In practice, we can compute only a finite number of terms in this series. This gives rise to a truncated map approximation of the original map. This truncated map is however not symplectic and can lead to wrong stability results when iterated. In this paper, following a generalization of the approach pioneered by Irwin (SSC Report No. 228, 1989), we factorize the map as a product of special maps called "jolt maps" in such a manner that symplecticity is maintained.

Item Type: Journal Article
Additional Information: Copyright of this article belongs to American Institute of Physics.
Department/Centre: Division of Physical & Mathematical Sciences > Centre for Theoretical Studies
Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 06 Dec 2006
Last Modified: 19 Sep 2010 04:33
URI: http://eprints.iisc.ernet.in/id/eprint/9098

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