C^k invariant manifolds for infinite delay
For a non-autonomous delay difference equation with infinite delay, we construct smooth stable and unstable invariant manifolds for any sufficiently small perturbation of an exponential dichotomy. We consider a general class of norms on the phase space satisfying an axiom considered by Matsunaga...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2019-04-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2019/50/abstr.html |
| Summary: | For a non-autonomous delay difference equation with infinite delay,
we construct smooth stable and unstable invariant manifolds for any
sufficiently small perturbation of an exponential dichotomy.
We consider a general class of norms on the phase space satisfying an
axiom considered by Matsunaga and Murakami that goes back to earlier work
by Hale and Kato for continuous time. In addition, we show that the
invariant manifolds are as regular as the perturbation. Finally, we
consider briefly the case of center manifolds and we formulate
corresponding results. |
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| ISSN: | 1072-6691 |