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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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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Cech cohomology; chain recurrent set; theorem by Conley; Lyapunov functions
Language:English
Date:2004
Deposited On:29 Nov 2010 16:26
Last Modified:06 Dec 2017 20:48
Publisher:Cambridge University Press
ISSN:0143-3857
Additional Information:© Cambridge University Press 2004
Publisher DOI:https://doi.org/10.1017/S0143385703000762
Related URLs:http://www.ams.org/mathscinet-getitem?mr=2104593

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