Singularly perturbed ordinary differential equations with nonautonomous fast dynamics

Journal of Dynamics and Differential Equations

Volumn 11, Issue 2, 1999, Pages 297-318

  Artstein, Zvi ^a  

^a WEIZMANN INSTITUTE OF SCIENCE   (Israel)

Author keywords

Invariant measures; Limiting equations; Singular perturbations; Skew product flows; Time varying equations

Indexed keywords

EID: 0007110738     PISSN: 10407294     EISSN: 15729222     Source Type: Journal    
DOI: 10.1023/A:1021981430215     Document Type: Article

References (20)

1. Artstein, Z. (1974). On the calculus of closed set-valued functions. Indiana Univ. Math. J. 24, 433-441.
2. Artstein, Z. (1977). Topological dynamics of an ordinary differential equation. J. Diff. Eq. 23, 216-223.
3. Artstein, Z. (1977). Topological dynamics of ordinary differential equations and Kurzweil equations. J. Diff. Eq. 23, 224-243.
4. Artstein, Z. (1977). The limiting equations of nonautonomous ordinary differential equations.J. Diff. Eq. 25, 184-202.
5. Artstein, Z. (1976). Limiting equations and stability of nonautonomous ordinary differential equations. In LaSalle, J. P., The Stability of Dynamical Systems, Region. Conf. Ser. Appl. Math., Vol. 25, SIAM Publications.
6. Artstein, Z., and Vigodner, A. (1996). Singularly perturbed ordinary differential equations with dynamic limits. Proc. Roy. Soc. Edinburgh 126A, 541 569.
7. Bhatia, N. P., and Szego, G. P. (1970). Stability Theory of Dynamical Systems, Springer-Verlag, Berlin.
8. Billingsley, P. (1968). Convergence of Probability Measures, Wiley, New York.
9. Bogoliubov, N. N., and Mitropolsky, Y. A. (1961). Asymptotic Methods in the Theory of Non-Linear Oscillations, Hindustan, Delhi.
10. Dafermos, C. M. (1974). Semillows associated with compact and uniform processes. Math. Syst. Theory 8, 142-145.
11. Kato, J., Martynyuk, A. A., and Shestakov, A., A. (1996). Stability of Motion of Non-autonomous Systems (Methods of Limiting Equations), Gordon and Breach, Luxembourg.
12. Klein, E., and Thompson, A. C. (1984). Theory of Correspondences, Wiley Interscience, New York.
13. Miller, R. K., and Sell, G. R. (1970). Volterra integral equations and topological dynamics. Mem. Am. Math. Soc. 102.
14. Nemytskii, V. V., and Stepanov, V. V. (1960). Qualitative Theory of Differential Equations, Princeton University Press, Princeton, NJ.
15. O'Malley, R. E., Jr. (1991). Singular Perturbation Methods for Ordinary Differential Equations, Springer-Verlag, New York.
16. Rockafellar, R. T. (1976). Integral functionals, normal integrands and measurable selections. In Waelbroeck, L. (ed.), Nonlinear Operators and the Calculus of Variations, Lecture Notes in Mathematics, Vol. 453, Springer-Verlag, Berlin, pp. 157-208.
17. Sell, G. R. (1967). Nonautonomous differential equations and topological dynamics, I and II. Trans. Am. Math. Soc. 127, 241 283.
18. Sell, G. R. (1971). Lectures on Topological Dynamics and Differential Equations, Van Nostrand-Reinhold, London.
19. Tikhonov, A. N., Vasiléva, A. B., and Sveshnikov, A. G. (1985). Differential Equations, Springer-Verlag, Berlin.
20. Wasow, W. (1965). Asymptotic Expansions for Ordinary Differential Equations, Wiley Interscience, New York.