Lyapunov 1-forms for flows

M. Farber; T. Kappeler; J. Latschev; E. Zehnder

doi:10.1017/S0143385703000762

Lyapunov 1-forms for flows

M. Farber^*
, T. Kappeler
, J. Latschev
, E. Zehnder

^*Corresponding author for this work

Durham University
University of Zurich
Humboldt University of Berlin
ETH Zurich - Institute for Particle Physics and Astrophysics (IPA)

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

In this paper 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 Čech cohomology class ξ ∼ Ȟ^⊥(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.

Original language	English
Pages (from-to)	1451-1475
Number of pages	25
Journal	Ergodic Theory and Dynamical Systems
Volume	24
Issue number	5
DOIs	https://doi.org/10.1017/S0143385703000762
State	Published - Oct 2004
Externally published	Yes

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title = "Lyapunov 1-forms for flows",

abstract = "In this paper 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 {\v C}ech cohomology class ξ ∼ Ȟ⊥(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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AU - Farber, M.

AU - Kappeler, T.

AU - Latschev, J.

AU - Zehnder, E.

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Y1 - 2004/10

N2 - In this paper 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 Čech cohomology class ξ ∼ Ȟ⊥(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.

AB - In this paper 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 Čech cohomology class ξ ∼ Ȟ⊥(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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ER -

Lyapunov 1-forms for flows

Abstract

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