期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：1977
卷号：74
期号：8
页码：3124-3125
DOI：10.1073/pnas.74.8.3124
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：We consider an almost periodic solution {varphi}(t) of an autonomous differential equation x' = f(x). Let k denote the topological dimension of the hull H({varphi}). By considering the linearized equation x' = A(t)x alone [where A(t) is the Jacobian matrix of f evaluated along {varphi}(t)], one can derive a sufficient condition in order that {varphi}(t) be quasi-periodic and that the hull H({varphi}) 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.
