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Lyapunov 1-forms for flows

Published online by Cambridge University Press:  18 October 2004

M. FARBER ,
T. KAPPELER ,
J. LATSCHEV  and
E. ZEHNDER
M. FARBER
Affiliation:
Department of Mathematics, University of Durham, Durham DH1 3LE, UK (e-mail: [email protected])
T. KAPPELER
Affiliation:
Institute of Mathematics, University of Zürich, 8057 Zürich, Switzerland (e-mail: [email protected])
J. LATSCHEV
Affiliation:
Institut für Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany (e-mail: [email protected])
E. ZEHNDER
Affiliation:
Department of Mathematics, ETH Zürich, 8092 Zürich, Switzerland (e-mail: [email protected])
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Abstract

In this paper we find conditions which guarantee that a given flow $\Phi$ on a compact metric space X admits a Lyapunov 1-form $\omega$ lying in a prescribed Čech cohomology class $\xi\in\check H^1(X;\mathbb{R})$. 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 by Conley about the existence of Lyapunov functions.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 24 , Issue 5 , October 2004 , pp. 1451 - 1475
Copyright
© 2004 Cambridge University Press

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