Hamiltonian dynamics on matched pairs
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CitationEsen, O. & Sütlü, S. S. (2016). Hamiltonian dynamics on matched pairs. International Journal of Geometric Methods in Modern Physics, 13(10), 1-24. doi:10.1142/S0219887816501280
The cotangent bundle of a matched pair Lie group, and its trivialization, are shown to be a matched pair Lie group. The explicit matched pair decomposition on the trivialized bundle is presented. On the trivialized space, the canonical symplectic two-form and the canonical Poisson bracket are explicitly written. Various symplectic and Poisson reductions are perfomed. The Lie–Poisson bracket is derived. As an example, Lie–Poisson equations on (Formula presented.) are obtained.