2023
DOI: 10.48550/arxiv.2302.14392
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Integrable multi-Hamiltonian systems from reduction of an extended quasi-Poisson double of $\operatorname{U}(n)$

Abstract: We construct a master dynamical system on a U(n) quasi-Poisson manifold, M d , built from the double U(n) × U(n) and d ≥ 2 open balls in C n , whose quasi-Poisson structures are obtained from T * R n by exponentiation. A pencil of quasi-Poisson bivectors P z is defined on M d that depends on d(d − 1)/2 arbitrary real parameters and gives rise to pairwise compatible Poisson brackets on the U(n)-invariant functions. The master system on M d is a quasi-Poisson analogue of the degenerate integrable system of free … Show more

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