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Proceedings of the American Mathematical Society

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

 

 

Dynamical systems whose orbit spaces are nearly Hausdorff


Author: Roger C. McCann
Journal: Proc. Amer. Math. Soc. 76 (1979), 258-262
MSC: Primary 54H20; Secondary 34C35, 54C35
DOI: https://doi.org/10.1090/S0002-9939-1979-0537084-5
MathSciNet review: 537084
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Abstract: Consider a continuous flow on a locally compact, separable, metric space. If the set of nonperiodic recurrent points is nowhere dense, then there is an open, dense, invariant subset of the phase space which has a Hausdorff orbit space. A separatrix is defined to be a trajectory which is in the closure of the set of trajectories at which the orbit space is not Hausdorff. If the flow is completely unstable, then the set of points which lie on separatrices is nowhere dense in the phase space.


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DOI: https://doi.org/10.1090/S0002-9939-1979-0537084-5
Keywords: Dynamical systems, orbit spaces, separatrix
Article copyright: © Copyright 1979 American Mathematical Society