2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65489In 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.27 pages, 3 figures. This revised version incorporates a few minor improvementsDynamical SystemsAlgebraic Topologytext