A.T. Fomenko & Nguyen Tien Zung, Topological classification of integrable nondegenerate Hamiltonians on a constant energy three-dimensional sphere. (Russian) Uspekhi Mat. Nauk 45 (1990), no. 6(276), 91–111, 189; translation in Russian Math. Surveys 45 (1990), no. 6, 109–135
A. T. Fomenko & Nguyen Tien Zung, Topological classification of integrable nondegenerate Hamiltonians on the isoenergy three-dimensional sphere. Topological classification of integrable systems, 267–296, Adv. Soviet Math., 6, Amer. Math. Soc., Providence, RI, 1991.
(no electronic file available)
The above 2 papers, written with A.T. Fomenko in 1990 while I was his undergraduate student in Moscow, were actually just one. When you were in Russia at that time, you were allowed to publish a paper in a Russian journal, and then send essentially the same paper to an English-language special volume somewhere else !
Though this paper is quite simple, it contains a very interesting class of knots in S3, which may be called “generalized torus” or “integrable” knots. Maybe due to the beauty of its simplicity, quite a few people liked the paper and cited it.
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- ! A.V. Bolsinov, A.T. Fomenko, Integrable Hamiltonian systems. Geometry, topology, classification, Chapman & Hall, 2004, 730 pp.
- Ghrist, Robert ; Kin, Eiko . Flowlines transverse to knot and link fibrations. Pacific J. Math. 217 (2004), no. 1, 61–86.
- G Goujvina, The Classification of the Bifurcations Emerging in the case of an Integrable Hamiltonian System with Two Degrees of Freedom when an Isoenergetic Surface is Non-Compact, Journal of Nonlinear Mathematical Physics, vol. 11 (2004), issue Supplement 1, p. 122.
- Robert Ghrist & Rafal Komendarczyk, Topological features of inviscid flows, in: An introduction to geometry and topology of fluid flows, edited by Renzo Ricca, NATO Sience Series, Vol. 47, 2001.
- ! A.V. Bolsinov, A.T. Fomenko, Integrable geodesic flows on two-dimensional surfaces, Kluwer Boston, 2000, 322 pp.
- Campos, B. ; Martínez Alfaro, J. ; Vindel, P. Bifurcations of links of periodic orbits in non-singular Morse-Smale systems with a rotational symmetry on $S^3$. Topology Appl. 102 (2000), no. 3, 279–295.
- Kidambi, Rangachari ; Newton, Paul K. Streamline topologies for integrable vortex motion on a sphere. Phys. D 140 (2000), no. 1-2, 95–125.
- Etnyre, John ; Ghrist, Robert . Contact topology and hydrodynamics. I. Beltrami fields and the Seifert conjecture. Nonlinearity 13 (2000), no. 2, 441–458.
- * Ouazzani-T. H, A.; Dekkaki, S.; Kharbach, J.; Ouazzani-Jamil, M. Bifurcation sets of the motion of a heavy rigid body around a fixed point in Goryatchev-Tchaplygin case. Nuovo Cimento Soc. Ital. Fis. B (12) 115 (2000), no. 10, 1175–1193.
- ** J. Etnyre, R. Ghrist, Stratified integrals and unknots in inviscid flows. Geometry and topology in dynamics (Winston-Salem, NC, 1998/San Antonio, TX, 1999), 99–111, Contemp. Math., 246, Amer. Math. Soc., Providence, RI, 1999.
- ** R. Ghrist, Chaotic knots and wild dynamics. Knot theory and its applications. Chaos Solitons Fractals 9 (1998), no. 4-5, 583–598.
- ! ** R. Ghrist, Ph. Holmes, M. Sullivan, Knots and links in three-dimensional flows. Lecture Notes in Mathematics, Vol. 1654, x+208 pp., 1997.
- ** AV Bolsinov, AT Fomenko, Application of classification theory for integrable Hamiltonian systems to geodesic flows on 2-sphere and 2-torus and to the description of the topological structure of momentum mapping near singular points, Journal of Mathematical Sciences, 78 (1996), No. 5.
- ** V.V. Kalashnikov, On genericity of integrable Hamiltonian systems of Bott type, Math. Sbornik 81 (1995)n No. 1.
- ** AV Bolsinov, AT Fomenko, Orbital classification of integrable Hamiltonian systems. Izvestya Mat. (1995).
- ** AV Bolsinov, VV Kozlov, AT Fomenko, The Maupertuis principle and geodesic flows on the sphere arising from integrable cases in the dynamics of a rigid body, Russian Math. Surveys 50 (1995), 473–501.
- ** K.N. Mishachev, Hamiltonian links in three-dimensional manifolds. Izv. Math. 59 (1995), no. 6, 1193–1205.
- ** L. Gavrilov & M. Ouazzani-Jamil & R. Caboz, Bifurcation diagrams and Fomenko’s surgery on Liouville tori of the Kolossoff potential $U=rho+(1/rho)-kcosphi$, Ann. Sci. École Norm. Sup. (4) 26 (1993), no. 5, 545–564
- ** VV Kalashnikov, Geometric description of minimax Fomenko invariants of integrable Hamiltonian systems on S3, RP3, S1 X S2, T3, Russian Math. Surveys 46 (1991), No. 4, 177.
- ^** Nguyen Tien Zung, L. S. Polyakova, E. N. Selivanova, “Topological Classification of Integrable Geodesic Flows on Orientable Two-Dimensional Riemannian Manifolds with Additional Integral Depending on Momenta Linearly or Quadratically”, Funct. Anal. Appl., 27:3 (1993), 186–196
- ^** Nguyen Tien Zung, “The complexity of integrable Hamiltonian systems on a prescribed three-dimensional constant-energy submanifold”, Russian Acad. Sci. Sb. Math., 75:2 (1993), 507–533