2002/10/31 by M. Farber, T. Kappeler, Farber, M. +5 · 1 citation
Mathematics · #Algebraic Topology (math.AT) #Dynamical Systems (math.DS) #FOS: Mathematics #math.AT #math.DS
paper · pdf · doi:10.48550/arxiv.math/0210473
27 pages, 3 figures. This revised version incorporates a few minor improvements
arxiv created 2003/02/10 · arxiv updated 2009/11/30
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∈ \check H1(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.