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- W2963867610 abstract "In this chapter we discuss a geometric approach to constructing integrable models. The starting point is a Poisson manifold with a rich group of symmetry transformations. Choosing an invariant hamiltonian and removing in a special way the degrees of freedom related to these symmetries, one obtains a new dynamical system on a smaller phase space which turns out to be integrable. The cotangent bundle of a Lie group and the Heisenberg double are representative examples of such Poisson manifolds with extended symmetries, and we explain their construction in great detail. Our discussion is paralleled by the treatment of the hamiltonian and Poisson reduction techniques, which we apply to these manifolds to obtain the integrable models of the CMS and RS type." @default.
- W2963867610 created "2019-07-30" @default.
- W2963867610 creator A5048607602 @default.
- W2963867610 date "2019-01-01" @default.
- W2963867610 modified "2023-09-27" @default.
- W2963867610 title "Integrability from Symmetries" @default.
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- W2963867610 doi "https://doi.org/10.1007/978-3-030-24198-8_2" @default.
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