Farber, M; Kappeler, T; Latschev, J; Zehnder, E (2004). Lyapunov 1-forms for flows. Ergodic Theory and Dynamical Systems, 24(5):1451-1475.
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.
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.
| Item Type: | Journal Article, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 510 Mathematics |
| Scopus Subject Areas: | Physical Sciences > General Mathematics
Physical Sciences > Applied 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: | 23 Jan 2022 14:35 |
| Publisher: | Cambridge University Press |
| ISSN: | 0143-3857 |
| Additional Information: | © Cambridge University Press 2004 |
| OA Status: | Green |
| Publisher DOI: | https://doi.org/10.1017/S0143385703000762 |
| Related URLs: | http://www.ams.org/mathscinet-getitem?mr=2104593 |
Farber, M