Dynamics of numerical approximations

Applied Mathematics and Computation

Volumn 89, Issue 1-3, 1998, Pages 5-15

  Hale, Jack K ^a  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 1042285852     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0096-3003(97)81644-X     Document Type: Article

References (17)

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2. J. K. Hale and G. Raugel, Lower semicontinuity of attractors of gradient systems and applications, Ann. Math. Pura Appl. 154:281-326 (1989).
3. J. K. Hale, X.-B Lin and G. Raugel, Upper semicontinuity of attractors for approximations of semigroups and partial differential equations, Math. Comp. 50:89-123 (1988).
4. A Stuart, Numerical analysis of dynamical systems, Acta Numerica, (1974).
5. F. Alouges and A. Debussche, On the discretization of a partial differential equation in the neighborhood of a period orbit, Numer. Math., 65:143-175 (1993).
6. B. Fiedler and J. Scheurle, Discretization of homoclinic orbits, rapid forcing and "invisible chaos", Mem. Am. Math. Soc. 570 (1996).
7. S.-N. Chow and J. K. Hale, Methods of Bifurcation Theory, Springer, 1982.
8. M. C. Irwin, On the stable manifold theorem, Bull. London Math. Soc., 2:196-198 (1970).
9. J. Palis, On Morse-Smale dynamical systems, Topology, 8:385-405 (1969).
10. J. Palis and S. Smale, Structural stability theorems, Global Analysis, Proc. Symp. Pure Math. 14 (1970).
11. M. Urabe, Nonlinear Autonomous Oscillations, Academic Press, 1967.
12. J. K. Hale, Ordinary Differential Equations, Krieger, 1980.
13. N. N. Bogoliubov and Y. A. Mitropolskii, Asymptotic Methods in the Theory of Nonlinear Oscillations, Gordon and Breach, 1961.
14. D. Henry, Geometric Theory of Semilinear Parabolic Equations, Lect. Notes Math. 840, Springer-Verlag (1981).
15. M. W. Hirsch, C. C. Pugh and M. Shub, Invariant Manifolds, Lect. Notes Math. 583, Springer-Verlag (1977).
16. F. Alouges and A. Debussche, On the qualitative behavior of the orbits of a parabolic partial differential equation in the neighborhood of a hyperbolic fixed point, Numer. Funct. Anal. and Optimiz., 12:253-269 (1991).
17. J. K. Hale and G. Raugel, Reaction-diffusion equation on thin domains, J. Math. Pures Appl., 71:33-95 (1992).