Hyperbolic almost periodic solutions and toroidal limit sets.
We consider an almost periodic solution phi(t) of an autonomous differential equation x' = f(x). Let k denote the topological dimension of the hull H(phi). By considering the linearized equation x' = A(t)x alone [where A(t) is the Jacobian matrix of f evaluated along phi(t)], one can derive a sufficient condition in order that phi(t) be quasi-periodic and that the hull H(phi) be diffeomorphic to a k-dimensional torus T(k). The proof is based upon an extension of the center manifold theorem to nonautonomous nonperiodic differential systems.
School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455.
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