2016•The Journal of Geometric MechanicsOpen access
No monodromy in the champagne bottle, or singularities of a superintegrable system
Larry Bates, Francesco Fassò
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Abstract
The three-dimensional champagne bottle system contains no mondromy, despitebeing entirely composed of invariant two-dimensional champagne bottle systems,each of which posesses nontrivial monodromy. We explain where the monodromywent in the three-dimensional system, or perhaps, where it did comefrom in the two-dimensional system, by regarding the three-dimensionalsystem not as completely integrable, but as superintegrable (ornon-commutatively integrable), and explaining the role of thesingularities of its isotropic-coisotropic pair of foliations.