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arXiv · 1905.13112

Rigid fibers of spinning tops

Morimichi Kawasaki·Ryuma Orita
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Abstract

(Non-)displaceability of fibers of integrable systems has been an important problem in symplectic geometry. In this paper, for a large class of classical Liouville integrable systems containing the Lagrangian top, the Kovalevskaya top and the C. Neumann problem, we find a non-displaceable fiber for each of them. Moreover, we show that the non-displaceable fiber which we detect is the unique fiber which is non-displaceable from the zero-section. As a special case of this result, we also show that a singular level set of a convex Hamiltonian is non-displaceable from the zero-section. To prove these results, we use the notion of superheaviness introduced by Entov and Polterovich.

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Morimichi Kawasaki, Ryuma Orita. 2019-05-30. Rigid fibers of spinning tops. https://arxiv.org/abs/1905.13112

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