The conjugacy of a discrete semidynamical system and its partially decoupled discrete semidynamical system in a Banach space is proved in a neighbourhood of the nontrivial invariant manifold.
"Conjugacy of a Discrete Semidynamical System in a Neighbourhood of the Nontrivial Invariant Manifold." Int. J. Differ. Equ. 2014 (SI1) 1 - 7, 2014. https://doi.org/10.1155/2014/703868