A convexity theorem for three tangled Hamiltonian torus actions,and super-integrable systems |
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Authors: | Hiraku Abe |
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Institution: | Department of Mathematics and Information of Science, Tokyo Metropolitan University, Minami-Ohsawa 1-1, Hachioji, Tokyo 192-0397, Japan |
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Abstract: | A completely integrable system on a symplectic manifold is called super-integrable when the number of independent integrals of motion is more than half the dimension of the manifold. Several important completely integrable systems are super-integrable: the harmonic oscillators, the Kepler system, the non-periodic Toda lattice, etc. Motivated by an additional property of the super-integrable system of the Toda lattice (Agrotis et al., 2006) 2], we will give a generalization of the Atiyah and Guillemin–Sternberg?s convexity theorem. |
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Keywords: | Symplectic manifolds Torus actions Convexity Super-integrable systems |
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