Skip to main content
SpringerLink
Log in

On surfaces defined by ordinary differential equations: A new approach to Hilbert’s 16th problem

  • Conference paper
  • First Online:
Ordinary and Partial Differential Equations

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1151))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. D. Hilbert, Mathematische Probleme, Gottingen Nachrichten (1900) 253–297.

    Google Scholar 

  2. Mathematical Developments Arising from Hilbert Problems, Vol. I and II, Proceedings of Symposia Pure Mathematics, Vol. 28 (1974).

    Google Scholar 

  3. H. Poincaré, Sur les courbes definies par des équations differentielles (1881–1886) OEUVRES de Henri Poincaré I.

    Google Scholar 

  4. Chin Yuan-Shun (Qin Yuanxun), Shi Song-Ling, Tsai Sui-Lin, On limit cycles of planar quadratic system, Scientia Sinica (1982) Series A, Vol. 25, 41–50.

    MathSciNet  Google Scholar 

  5. I.G. Petrovskii and E.M. Landis, On the number of limit cycles of the equation dy/dx = P(x,y)/Q(x,y), where P and Q are polynomials of the second degree, Mat. Sb.N.S. 37 (79) (1955), 209–250 (in Russian); Amer. Math. Soc. Transl. (2) 10 (1958) 177–221.

    MathSciNet  Google Scholar 

  6. N.N. Molchanov, The use of the theory of continuous groups of transformations in investigating the solutions of ordinary differential equations, Dokl. Akad. Nauk SSSR(N,S,) 112 (1957) 998–1001 (in Russian).

    MathSciNet  MATH  Google Scholar 

  7. Chin Yuan-Shun, Qualitative Theory of Ordinary Differential Equations in Complex Domain, I.II.III. (in Chinese) Research and Applications of Mathematics, Institute of Applied Mathematics, Academia Sinica, No. 4 (1979), 17–33; No. 5 (1979) 18–48; No. 1 (1980) 15–36. Also see Journal of Northwest University No. 3 (1982) 1–18.

    Google Scholar 

  8. Chin Yuan-Shun, Uber den Differentialgleichungen mit algebraishen Grenzzyklen zweiter Ordnung. Science Record N.S.I.2. (1957) Academia Sinica.

    Google Scholar 

  9. N.N. Bautin, On the number of limit cycles which appear with the variation of coefficients from an eqilibrium position of focus or centre type, Mat. Sb.N.S. 30 (72) (1952) 181–196 (in Russian); Amer. Math. Soc. Transl. No. 100 (1954), and in Amer. Math. Soc. Transl. (1) 5 (1962) 396–413.

    MathSciNet  Google Scholar 

  10. Chin Yuan-Shun, Pu Fu-Chung, Concrete example of three limit cycles appearing in the neighbourhood of a singular point of a quadratic system dx/dt = P, dy/dt = Q. Mathematica Sinica Vol.9 (1959) 213–226.

    Google Scholar 

  11. Chin Yuan-Shun (Qin Yuanxun) So Guan-Jan, Du Xun-Fu, On limit cycles of planar quadratic system II, Scientia Sinica (1983) Series A Vol. 26 (1983) 1025–1038.

    Google Scholar 

  12. L. Bieberbach, Theorie Der Gewohlichen Differential Gleichungen (1953).

    Google Scholar 

  13. Qin Jen-Sui, Limit Cycle Producing Program System, (1983) (To be published).

    Google Scholar 

  14. Qin, Chao-Bin, numerical method for calculation of two dimensional surfaces in four dimensional space in connection with solution of ordinary differential equations in complex domain, (1981) (To be published).

    Google Scholar 

Download references

Authors
  1. Yuan-Shun Chin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yuanxun Qin
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Brian D. Sleeman Richard J. Jarvis

Rights and permissions

Reprints and permissions

Copyright information

© 1985 Springer-Verlag

About this paper

Cite this paper

Chin, YS., Qin, Y. (1985). On surfaces defined by ordinary differential equations: A new approach to Hilbert’s 16th problem. In: Sleeman, B.D., Jarvis, R.J. (eds) Ordinary and Partial Differential Equations. Lecture Notes in Mathematics, vol 1151. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074720

Download citation

  • DOI: https://doi.org/10.1007/BFb0074720

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15694-9

  • Online ISBN: 978-3-540-39640-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation