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Transactions of the American Mathematical Society

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Nonstandard analysis of dynamical systems. I. Limit motions, stability.


Author: A. E. Hurd
Journal: Trans. Amer. Math. Soc. 160 (1971), 1-26
MSC: Primary 34.65
DOI: https://doi.org/10.1090/S0002-9947-1971-0280827-6
MathSciNet review: 0280827
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Abstract: The methods of nonstandard analysis are applied to the study of the qualitative theory of dynamical systems. The nonstandard notions connected with limiting behavior of motions (limit sets, etc.) are developed, and then applied to the study of stability theory, including stability of sets, attracting properties, first prolongations and stability of motions.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1971-0280827-6
Keywords: Dynamical systems, limit motions, stability, nonstandard analysis
Article copyright: © Copyright 1971 American Mathematical Society