Geodesic
Smale--Fomenko diagrams and rough topological invariants of the Kowalevski--Yehia case
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 4 (2011), pp. 40-59

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We present the complete analytical classification of the atoms arising at the critical points of rank 1 of the Kowalevski–Yehia gyrostat. To classify the Smale–Fomenko diagrams, all separating values of the gyrostatic momentum are found. We present a kind of constructor of the Fomenko graphs; its application gives the complete description of the rough topology of this integrable case. It is proved that there exists exactly nine groups of identical molecules (not considering the marks). These groups contain 22 stable types of graphs and 6 unstable ones with respect to the number of critical circles on the critical levels.
Keywords: gyrostat, Kowalevski–Yehia case, diagrams, topological invariants. 
@article{VUU_2011_4_a3,
     author = {M. P. Kharlamov and P. E. Ryabov},
     title = {Smale--Fomenko diagrams and rough topological invariants of the {Kowalevski--Yehia} case},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {40--59},
     publisher = {mathdoc},
     number = {4},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2011_4_a3/}
}
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M. P. Kharlamov; P. E. Ryabov. Smale--Fomenko diagrams and rough topological invariants of the Kowalevski--Yehia case. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 4 (2011), pp. 40-59. http://geodesic.mathdoc.fr/item/VUU_2011_4_a3/