Morse spectrum for nonautonomous differential equations
- The concept of a Morse decomposition consisting of nonautonomous sets is reviewed for linear cocycle mappings w.r.t. past, future and all-time convergences. In each case, the set of accumulation points of the finite-time Lyapunov exponents corresponding to points in a nonautonomous set is shown to be an interval. For a finest Morse decomposition, the Morse spectrum is defined as the union of all of the above accumulation point intervals over the different nonautonomous sets in such a finest Morse decomposition. In addition, Morse spectrum is shown to be independent of which finest Morse decomposition is used, when more than one exists.
| Author: | Fritz ColoniusORCiDGND, Peter Kloeden, Martin RasmussenORCiDGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-8938 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/1044 |
| Series (Serial Number): | Preprints des Instituts für Mathematik der Universität Augsburg (2008-25) |
| Type: | Preprint |
| Language: | English |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2008/06/30 |
| Tag: | Morse-Zerlegung Ljapunov exponent; Morse decomposition; nonautonomous system |
| GND-Keyword: | Ljapunov-Exponent; Nichtautonomes System; Ljapunov-Spektrum; Morse-Theorie |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehr- und Forschungseinheit Angewandte Analysis | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
