# Smooth Lyapunov 1-forms

Farber, M; Kappeler, T; Latschev, J; Zehnder, E (2004). Smooth Lyapunov 1-forms. L'Enseignement Mathématique. Revue Internationale. 2e Série, 50(1-2):3-17.

## Abstract

We find conditions which guarantee that a given flow O on a closed smooth manifold M admits a smooth Lyapunov 1-form u lying in a prescribed de Rham cohomology class £ 6 Hx (M; R). These conditions are formulated in terms of Schwartzman's asymptotic cycles A^($>) 6 //i(M;R) of the flow. We find conditions which guarantee that a given flow O on a closed smooth manifold M admits a smooth Lyapunov 1-form u lying in a prescribed de Rham cohomology class £ 6 Hx (M; R). These conditions are formulated in terms of Schwartzman's asymptotic cycles A^($>) 6 //i(M;R) of the flow.