Abstract
A theory of double families of evolution operators, which involves mappings between different spaces, is presented. Causality is in a form analogous to that in integrated semi-groups, but involves an integrated relationship between members of both families. The approach is from a dynamic systems point of view, and focuses very much on the trajectories defined by the evolution operators and their relationship to the solutions of implicit evolution equations. Illustrative examples concerned with dynamic boundary conditions are provided.
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