Relative structure cycles and the existence of smooth Lyapunov 1-forms for flows

Mathematics – Geometric Topology

Scientific paper

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20 pages

Scientific paper

We give necessary and sufficient conditions for the existence of smooth
Lyapunov 1-forms for the flow of a smooth vector field in terms of the behavior
of certain locally finite invariant measures. The main statement generalizes a
result of Schwartzman, whereas the methods are adapted from work of Sullivan.

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