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Two-system of a Hamiltonian system

M. F. Kondratieva·S. Yu. Sadov
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Abstract

For a Hamiltonian system in R^{2n}, its two-system is defined in the phase space R^{2n} x sp(2n,R). In a sense, it is a combination of the original system and its system in variations with feedback. We study the Hamiltonian forms of the two-system and its analogs. In particular, we show a relation between the Poisson-Lie bracket on the (dual space to) Lie algebra sp(2n,R) and the canonical bracket.

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M. F. Kondratieva, S. Yu. Sadov. 2004-10-09. Two-system of a Hamiltonian system. https://arxiv.org/abs/math/0410237

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