Advertisement

Mathematical systems theory

, Volume 1, Issue 4, pp 353–372 | Cite as

Invariance for ordinary differential equations

  • James A. Yorke
Article

Keywords

Differential Equation Ordinary Differential Equation Computational Mathematic 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    J. Auslander andP. Seibert, Prolongations in dynamical systems.Ann. Inst. Fourier (Grenoble) 14 (1964), Fasc. 2, 236–267.Google Scholar
  2. [2]
    E. A. Coddington andN. Levinson,Theory of Ordinary Differential Equations, McGraw-Hill, New York, 1955.Google Scholar
  3. [3]
    P. Hartman,Ordinary Differential Equations, Wiley, New York, 1964.Google Scholar
  4. [4]
    S. Lefschetz, Liapunov and stability in dynamical systems,Bol. Soc. Mat. Mexicana 3 (1958), 25–39.Google Scholar
  5. [5]
    L. Markus, Asymptotically autonomous differential systems,Ann. of Math. Studies, No. 36, 17–29.Google Scholar
  6. [6]
    Z. Opial, Sur la dépendance des solutions d'un système d'équations différentielles de leurs seconds membres,Ann. Polonici Math. 8 (1960), 75–89.Google Scholar
  7. [7]
    G. Peano, Démonstration de l'intégrabilité des équations différentielles ordinaires,Math. Ann. 37 (1890), 182–228.Google Scholar
  8. [8]
    W. Pervin,Foundations of General Topology, Academic Press, New York, 1964.Google Scholar
  9. [9]
    E. Roxin, Stability in general control systems,J. Diff. Equations 1 (1965), 115–150.Google Scholar
  10. [10]
    A. Strauss andJ. A. Yorke, On asymptotically autonomous differential equations,Math. Systems Theory 1 (1967), 175–182.Google Scholar
  11. [11]
    T. Yoshizawa, Asymptotic behavior of solutions of a system of differential equations,Contributions to Differential Equations 1 (1963), 371–387.Google Scholar
  12. [12]
    T. Yoshizawa, Stability theory by Liapunov's second method,J. Math. Soc. Japan (1966).Google Scholar
  13. [13]
    J. Massera, Contributions to stability theory,Ann. Math. 64 (1956), 182–206.Google Scholar
  14. [14]
    M. Fukuhara (= Hukuhara), Sur les systèmes des équations différentielles ordinaires II,Jap. J. Math. 6 (1930), 269–299.Google Scholar
  15. [15]
    E. Roxin andV. Spinadel, Reachable zones in autonomous differential systems,Contributions to Differential Equations 1 (1963), 275–315.Google Scholar
  16. [16]
    J. Kato andA. Strauss, On the global existence of solutions and Liapunov functions,Ann. Mat. Pura Appl., to appear.Google Scholar
  17. [17]
    M. Nagumo, Über die Lage der Integralkurven gewöhnlicher Differentialgleichungen,Proc. Phys.-Math. Soc. Japan 24 (1942) 551–559.Google Scholar
  18. [18]
    R. K. Miller, Asymptotic behavior of nonlinear delay-differential equations,J. Differential Equations 1 (1965), 293–305.Google Scholar
  19. [19]
    M. Hukuhara, Sur la théorie des équations différentielles ordinaires,J. Faculty Sci., U. of Tokyo, Sec. I,7 (1958), 483–510.Google Scholar

Copyright information

© Springer-Verlag New York Inc 1967

Authors and Affiliations

  • James A. Yorke
    • 1
  1. 1.Institute for Fluid Dynamics and Applied MathematicsUniversity of MarylandCollege ParkUSA

Personalised recommendations