Invariant manifolds for Volterra integral equations of convolution type

In this paper we develop some elements of a qualitative theory for nonlinear Volterra integral equations of convolution type. Our starting point is a local semiflow associated with the equation and acting on a space of compactly supported forcing functions. Within that framework we discuss the variation-of-constants formula, the saddle point property, the center manifold and Hopf bifurcation. Some equations from population biology get special attention.