Two-system of a Hamiltonian system
M. F. Kondratieva, S. Yu. Sadov
Abstract
For a Hamiltonian system in R2n, its two-system is defined in the phase space R2n 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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