A Hartman-Grobman Theorem for a Class of Retarded Functional Differential Equations

A local stability theorem, an analog of the Hartman-Grobman Theorem, is formulated and proved for retarded functional differential equations with a compact attractor and a solution map that is one-to-one on the attractor. The result that is obtained is directly applicable to analytic retarded functional differential equations with a compact attractor, to dissipative retarded functional differential equations with a continuous attractor, as well as to arbitrary retarded functional differential equations with a compact, continuous, uniformly asymptotically stable attractor.