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arXiv · 1606.03868

Partially superintegrable systems on Poisson manifolds

A. Kurov·G. Sardanashvily
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Abstract

Superintegrable systems on a symplectic manifold conventionally are considered. However, their definition implies a rather restrictive condition 2n=k+m where 2n is a dimension of a symplectic manifold, k is a dimension of a pointwise Lie algebra of a superintegrable system, and m is its corank. To solve this problem, we aim to consider partially superintegrable systems on Poisson manifolds where k+m is the rank of a compatible Poisson structure. The according extensions of the Mishchenko-Fomenko theorem on generalized action-angle coordinates is formulated.

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A. Kurov, G. Sardanashvily. 2016-06-13. Partially superintegrable systems on Poisson manifolds. https://doi.org/10.1088/1742-6596%2F804%2F1%2F012025

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