Local sections of flows on manifolds

Chewning, William C.; Owen, R. Steven

doi:10.1090/S0002-9939-1975-0362404-0

Local sections of flows on manifolds
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by William C. Chewning and R. Steven Owen PDF

Proc. Amer. Math. Soc. 49 (1975), 71-77 Request permission

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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