Lyapunov 1-forms for flows

Farber, M; Kappeler, T; Latschev, J; Zehnder, E (2004). Lyapunov 1-forms for flows. Ergodic Theory and Dynamical Systems, 24(5):1451-1475.

Abstract

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 Cech cohomology class ξ∈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 by Conley about the existence of Lyapunov functions.

Abstract

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 Cech cohomology class ξ∈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 by Conley about the existence of Lyapunov functions.

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