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Lyapunov 1-forms for flows

M. Farber·T. Kappeler·J. Latschev·E. Zehnder
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Abstract

In this paper we find conditions which guarantee that a given flow $Φ$ on a compact metric space $X$ admits a Lyapunov one-form $ω$ lying in a prescribed Čech cohomology class $ξ\in \check H^1(X;\R)$. These conditions are formulated in terms of the restriction of $ξ$ to the chain recurrent set of $Φ$. The result of the paper may be viewed as a generalization of a well-known theorem of C. Conley about the existence of Lyapunov functions.

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M. Farber, T. Kappeler, J. Latschev, E. Zehnder. 2003-02-10. Lyapunov 1-forms for flows. https://arxiv.org/abs/math/0210473

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