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Proceedings of the American Mathematical Society

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Dynamical systems satisfying certain stability and recursive criteria


Author: Ronald A. Knight
Journal: Proc. Amer. Math. Soc. 85 (1982), 373-380
MSC: Primary 54H20; Secondary 58F25
DOI: https://doi.org/10.1090/S0002-9939-1982-0656106-4
MathSciNet review: 656106
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Abstract: A necessary and sufficient condition for the various characteristic zero concepts to coincide is given. We prove that on locally compact spaces a flow of characteristic 0 and the center of a flow of characteristic $ {0^ + }$ are almost of characteristic $ {0^ \pm }$. Poisson stable flows and nonwandering flows of the zero characteristics are characterized in terms of the prolongation, prolongational limit, orbit closure, limit, and weak attraction relations. Examples showing the results are sharp are given.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0656106-4
Keywords: Center, divergent, dispersive, dynamical system, flow, minimal, nonwandering, Poisson stable, recurrent, stability, weak attraction, zero characteristic
Article copyright: © Copyright 1982 American Mathematical Society

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