Luis Barreira, Claudia Valls
Abstract:
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.
Submitted May 7, 2018. Published April 17, 2019.
Math Subject Classifications: 37D10.
Key Words: Difference equations; infinite delay; invariant manifolds.
Show me the PDF file (316 KB), TEX file for this article.
| Luis Barreira Departamento de Matemática Instituto Superior Técnico Universidade de Lisboa 1049-001 Lisboa, Portugal email: barreira@math.tecnico.ulisboa.pt |
|
Claudia Valls Departamento de Matemática Instituto Superior Técnico Universidade de Lisboa 1049-001 Lisboa, Portugal email: cvalls@math.tecnico.ulisboa.pt |
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