The Hess–Appelrot case and quantization of the rotation number
2017, Vol. 13, No. 3, pp. 433-452
Author(s): Bizyaev I. A., Borisov A. V., Mamaev I. S.
This paper is concerned with the Hess case in the Euler–Poisson equations and with its
generalization on the pencil of Poisson brackets. It is shown that in this case the problem reduces
to investigating the vector field on a torus and that the graph showing the dependence of the
rotation number on parameters has horizontal segments (limit cycles) only for integer values of
the rotation number. In addition, an example of a Hamiltonian system is given which possesses
an invariant submanifold (similar to the Hess case), but on which the dependence of the rotation
number on parameters is a Cantor ladder.
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