Dichotomy spectra and Morse decompositions of linear nonautonomous differential equations
- Recently, the existence of Morse decompositions for nonautonomous dynamical systems was shown for three different time domains: the past, the future and, in the linear case, the entire time. In this article, notions of exponential dichotomy are discussed with respect to the three time domains. It is shown that an exponential dichotomy gives rise to an attractor-repeller pair in the projective space, which is a building block of a Morse decomposition. Moreover, based on the notions of exponential dichotomy, dichotomy spectra are introduced, and it is proved that the corresponding spectral manifolds lead to Morse decompositions in the projective space.
| Author: | Martin RasmussenORCiDGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-4921 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/619 |
| Series (Serial Number): | Preprints des Instituts für Mathematik der Universität Augsburg (2008-03) |
| Type: | Preprint |
| Language: | English |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2008/02/01 |
| Tag: | Attractor; Attractor-repeller pair; Dichotomy spectrum; Exponential dichotomy; Finest Morse decomposition; Morse decomposition |
| GND-Keyword: | Attraktor; Repellor; Dichotomie; Morse-Theorie; Nichtautonomes System; Linear-homogene Differentialgleichung |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
