Dynamical systems satisfying certain stability and recursive criteria

Knight, Ronald A.

doi:10.1090/S0002-9939-1982-0656106-4

Dynamical systems satisfying certain stability and recursive criteria
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Proc. Amer. Math. Soc. 85 (1982), 373-380 Request permission

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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