Rational S1-equivariant homotopy theory

We give an algebraicization of rational S-1-equivariant homotopy theory. There is an algebraic category of "T-systems" which is equivalent to the homotopy category of rational S-1-simply connected S-1-spaces. There is also a theory of "minimal models" for T-systems, analogous to Sullivan's minimal algebras. Each S-1-space has an associated minimal T-system which encodes all of its rational homotopy information, including its rational equivariant cohomology and Postnikov decomposition.