Electronic Journal of Differential Equations,
Vol. 2019 (2019), No. 50, pp. 1-15.

Title: C^k invariant manifolds for infinite delay

Authors: Luis Barreira (Univ. de Lisboa, Portugal)
         Claudia Valls (Univ. de Lisboa, Portugal)
 
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.