Geodesic
The Hess–Appelrot case and quantization of the rotation number
Russian journal of nonlinear dynamics, Tome 13 (2017) no. 3, pp. 433-452

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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.
Keywords: invariant submanifold, rotation number, Cantor ladder
Mots-clés : limit cycles. 
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     title = {The {Hess{\textendash}Appelrot} case and quantization of the rotation number},
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     pages = {433--452},
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I. A. Bizyaev; A. V. Borisov; I. S. Mamaev. The Hess–Appelrot case and quantization of the rotation number. Russian journal of nonlinear dynamics, Tome 13 (2017) no. 3, pp. 433-452. http://geodesic.mathdoc.fr/item/ND_2017_13_3_a9/