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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Perturbed asymptotically stable sets

Author: Roger C. McCann
Journal: Proc. Amer. Math. Soc. 35 (1972), 107-111
MSC: Primary 34C40
MathSciNet review: 0296447
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Abstract: Perturbations of a dynamical system are defined and the behavior of compact asymptotically stable sets under these perturbations is determined. The occurrence of critical points in a perturbed planar dynamical system is also investigated.

References [Enhancements On Off] (What's this?)

  • [1] Roger C. McCann, Local sections of perturbed local dynamical systems, J. Differential Equations 10 (1971), 336–344. MR 0288746
  • [2] Otomar Hájek, Dynamical systems in the plane, Academic Press, London-New York, 1968. MR 0240418
  • [3] J. Auslander and P. Seibert, Prolongations and stability in dynamical systems, Ann. Inst. Fourier (Grenoble) 14 (1964), no. fasc. 2, 237–267. MR 0176180
  • [4] Nam P. Bhatia, Dynamical systems, Mathematical systems theory and economics, I, II (Proc. Internat. Summer School, Varenna, 1967) Springer, Berlin, 1969, pp. 1–9. Lecture Notes in Operations Research and Mathematical Economics, Vols. 11, 12. MR 0324143

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Keywords: Dynamical systems, perturbation asymptotic stability, stable critical point
Article copyright: © Copyright 1972 American Mathematical Society