In our book published in 1984 An Introduction to Infinite Dimensional Dynamical Systems-Geometric Theory, we presented some aspects of a geometric theory of infinite dimensional spaces with major emphasis on retarded
functional differential equations. In this book, the intent is the same. There
are new results on Morse–Smale systems for semiflows, persistence of hyperbolicity under perturbations, nonuniform hyperbolicity, monotone dynamical
systems, realization of vector fields on center manifolds and normal forms.
In addition, more attention is devoted to neutral functional differential equations although the theory is much less developed. Some parts of the theory
also will apply to many other types of equations and applications