Cm-smoothness of invariant fiber bundles for dynamic equations on measure chains
- We present a new self-contained and rigorous proof of the smoothness of invariant fiber bundles for dynamic equations on measure chains or time scales. Here, an invariant fiber bundle is the generalization of an invariant manifold to the nonautonomous case. Our main result generalizes the “Hadamard-Perron theorem” to the time-dependent, infinite-dimensional, noninvertible, and parameter-dependent case, where the linear part is not necessarily hyperbolic with variable growth rates. As a key feature, our proof works without using complicated technical tools.
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| Author: | Christian Pötzsche, Stefan Siegmund |
|---|---|
| URN: | urn:nbn:de:hebis:30-75571 |
| DOI: | https://doi.org/10.1155/S1687183904308010 |
| ISSN: | 1687-1847 |
| ISSN: | 1687-1839 |
| Parent Title (English): | Advances in difference equations |
| Publisher: | Hindawi |
| Place of publication: | New York, NY |
| Document Type: | Article |
| Language: | English |
| Year of Completion: | 2004 |
| Date of first Publication: | 2004/05/13 |
| Publishing Institution: | Universitätsbibliothek Johann Christian Senckenberg |
| Release Date: | 2010/03/09 |
| Volume: | 1 |
| Issue: | 2 |
| Page Number: | 42 |
| First Page: | 141 |
| Last Page: | 182 |
| Note: | Copyright © 2004 Hindawi Publishing Corporation |
| Source: | Advances in Difference Equations, vol. 2004, no. 2, pp. 141-182, 2004. doi:10.1155/S1687183904308010 ; http://www.hindawi.com/journals/ade/2004/572930.abs.html |
| HeBIS-PPN: | 221786961 |
| Institutes: | Informatik und Mathematik / Mathematik |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Licence (German): |  Deutsches Urheberrecht |
