Lyapunov 1-forms for flows

Details Lyapunov 1-forms for flows Lyapunov 1-forms for flows

2002-10-31

arxiv.org/abs/math/0210473v2

Mathematics

Dynamical Systems

27 pages, 3 figures. This revised version incorporates a few minor improvements

Scientific paper

In this paper we find conditions which guarantee that a given flow $\Phi$ on a compact metric space $X$ admits a Lyapunov one-form $\omega$ lying in a prescribed \v{C}ech cohomology class $\xi\in \check H^1(X;\R)$. These conditions are formulated in terms of the restriction of $\xi$ to the chain recurrent set of $\Phi$. 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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