Rigid fibers of integrable systems on cotangent bundles

Morimichi Kawasaki, Ryuma Orita
Journal of the Mathematical Society of Japan, vol. 74 (2022), no. 3, pp. 829–847
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Abstract
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(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 the existence of a singular level set of a convex Hamiltonian, which is non-displaceable from the zero-section. To prove these results, we use the notion of superheaviness introduced by Entov and Polterovich.

BibTeX

@article{kawasaki2022rigid,
  author        = {Kawasaki, Morimichi and Orita, Ryuma},
  title         = {{Rigid fibers of integrable systems on cotangent bundles}},
  journal       = {Journal of the Mathematical Society of Japan},
  volume        = {74},
  number        = {3},
  pages         = {829--847},
  year          = {2022},
  doi           = {10.2969/jmsj/84278427},
  eprint        = {1905.13112},
  archivePrefix = {arXiv}
}

Abstract#

Abstract
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