Skip to main content

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

Part of the Lecture Notes in Mathematics book series (LNM,volume 1453)

Keywords

  • Hamiltonian System
  • Euler Characteristic
  • Symplectic Manifold
  • Morse Function
  • Klein Bottle

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

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

    CrossRef  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.

    CrossRef  MathSciNet  MATH  Google Scholar 

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

    CrossRef  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.

    CrossRef  MathSciNet  Google Scholar 

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

    CrossRef  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.

    CrossRef  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1990 Springer-Verlag

About this chapter

Cite this chapter

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

Download citation

  • DOI: https://doi.org/10.1007/BFb0085946

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53407-5

  • Online ISBN: 978-3-540-46861-5

  • eBook Packages: Springer Book Archive