Negatively invariant sets of compact maps and an extension of a theorem of Cartwright

AbstractLet T be a C1 map from an open subset of a separable Hilbert space into the Hilbert space, and Γ a negatively invariant compact set, that is T(Γ) ⊇ Γ. Suppose the derivative of T for x ϵ Γ is a uniform contraction on a subspace of finite codimension. Then the topological dimension of Γ is finite. This result may be used to show that for certain delay differential equations and partial differential equations, any almost periodic solution has only finitely many rationally independent frequencies, thus extending results of Cartwright for ODE's