Lyapunov 1-forms for flows

M. Farber, T. Kappeler, J. Latschev, E. Zehnder

Research output: Contribution to journalArticlepeer-review


In this paper we find conditions which guarantee that a given flow Φ on a compact metric space X admits a Lyapunov 1-form ω lying in a prescribed Čech cohomology class ξ ∼ Ȟ(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 by Conley about the existence of Lyapunov functions.

Original languageEnglish
Pages (from-to)1451-1475
Number of pages25
JournalErgodic Theory and Dynamical Systems
Issue number5
StatePublished - Oct 2004
Externally publishedYes


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