Hyperbolic almost periodic solutions and toroidal limit sets

AUTOR(ES)

Sell, George R.

RESUMO

We consider an almost periodic solution φ(t) of an autonomous differential equation x′ = f(x). Let k denote the topological dimension of the hull H(φ). By considering the linearized equation x′ = A(t)x alone [where A(t) is the Jacobian matrix of f evaluated along φ(t)], one can derive a sufficient condition in order that φ(t) be quasi-periodic and that the hull H(φ) be diffeomorphic to a k-dimensional torus Tk. The proof is based upon an extension of the center manifold theorem to nonautonomous nonperiodic differential systems.

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