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Exact round morse functions, inequalities of morse type and integrals of Hamiltonian systems

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Book cover Global Analysis - Studies and Applications IV

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References

  1. Bott R. Non-degenerate critical manifolds. Ann. of Math., 1954, vol. 60, p. 248–261.

    Article  MathSciNet  MATH  Google Scholar 

  2. Fomenko A.T. Morse theory of integrable Hamiltonian systems. DAN, 1986, vol. 287, No 5, p. 1071–1075 (in Russian; see English translation in Soviet Math. Doklady).

    MathSciNet  MATH  Google Scholar 

  3. Fomenko A.T. The topology of constant energy surfaces of Hamiltonian systems and obstructions to integrability. Izvestiya AN SSSR, ser. Mat., 1986, vol. 50, No 6, p. 1276–1307 (in Russian; see English translation in Math. of the USSR — Izvestiya).

    MathSciNet  MATH  Google Scholar 

  4. Fomenko A.T., Zieschang H. On the topology of three-dimensional manifolds arising in Hamiltonian mechanics. DAN, 1987, vol. 294, No 2 (in Russian; see English translation in Soviet Math.-Doklady).

    Google Scholar 

  5. Asimov D. Round handles and non-singular Morse-Smale flows. Ann. of Math., 1975, vol. 102, No 1, p. 41–54.

    Article  MathSciNet  MATH  Google Scholar 

  6. Miyoshi S. Foliated round surgery of codimension — one foliated manifolds. Topology, 1983, vol. 21, No 3, p. 245–262.

    Article  MathSciNet  MATH  Google Scholar 

  7. Frunks J. The periodic structure of non-singular Morse-Smale flows. Comment. Math. Helv., 1978, vol. 53, No 2, p. 279–294.

    Article  MathSciNet  Google Scholar 

  8. Thurston W. Existence of codimension-one foliation. Ann. of Math., 1976, vol. 104, No 2, p. 249–268.

    Article  MathSciNet  MATH  Google Scholar 

  9. Oshemkov A.A. Bott integrals of certain integrable Hamiltonian systems. In: Geometriya, differentsial'nye uravneniya i mekhanika. Moscow, 1986, p. 115–117 (in Russian).

    Google Scholar 

  10. Matveev S.V., Fomenko A.T., Sharko V.V. Round Morse functions and isoenergetic surfaces of integrable Hamiltonian systems. Preprint No 86-76 of the Institute of Mathematics, Acad. Sci. of Ukr. SSR, Kiev, 1986 (in Russian).

    MATH  Google Scholar 

  11. Sharko V.V. Exact Morse functions on simply connected manifolds with simply connected boundary. Uspekhi Mat. Nauk, 1981, t. 36, No 5, p. 205–206 (in Russian; see English translation in Russian Math. Surveys).

    MathSciNet  MATH  Google Scholar 

  12. Trofimov V.V., Fomenko A.T. Liouville integrability of Hamiltonian systems on Lie algebras. Uspekhi Mat. Nauk, 1984, vol. 39, No 2, p. 3–56 (in Russian; see English translation in Russian Math. Surveys).

    MathSciNet  MATH  Google Scholar 

  13. Fomenko A.T. Topological variational problems. Moscow, 1984 (in Russian).

    Google Scholar 

  14. Smale S. On structure of manifolds. Amer. J. Math., 1962, vol. 84, No 3, p. 387–399.

    Article  MathSciNet  MATH  Google Scholar 

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Yurii G. Borisovich Yurii E. Gliklikh A. M. Vershik

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© 1990 Springer-Verlag

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Fomenko, A.T., Sharko, V.V. (1990). Exact round morse functions, inequalities of morse type and integrals of Hamiltonian systems. In: Borisovich, Y.G., Gliklikh, Y.E., Vershik, A.M. (eds) Global Analysis - Studies and Applications IV. Lecture Notes in Mathematics, vol 1453. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0085946

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