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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Local sections of flows on manifolds


Authors: William C. Chewning and R. Steven Owen
Journal: Proc. Amer. Math. Soc. 49 (1975), 71-77
MSC: Primary 58F10; Secondary 34C35
MathSciNet review: 0362404
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Abstract: We show the existence of local sections for dynamical systems on manifolds which are themselves generalized manifolds of codimension one. One implication of this is that the level surfaces of Lyapunov functions on three-manifolds are two-manifolds. This fact is used to study the geometry of stable attractors in three-manifolds.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0362404-0
PII: S 0002-9939(1975)0362404-0
Keywords: Local sections, stable attractors
Article copyright: © Copyright 1975 American Mathematical Society