Dynamical systems whose orbit spaces are nearly Hausdorff
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- by Roger C. McCann PDF
- Proc. Amer. Math. Soc. 76 (1979), 258-262 Request permission
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.References
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Additional Information
- © Copyright 1979 American Mathematical Society
- 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