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Affine-periodic solutions by averaging methods
Authors:Jiamin Xing  Xue Yang  Yong Li
Institution:1.College of Mathematics, Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education,Jilin University,Changchun,China;2.School of Mathematics and Statistics,Northeast Normal University,Changchun,China;3.Center for Mathematics and Interdisciplinary Sciences,Northeast Normal University,Changchun,China
Abstract:This paper concerns the existence of affine-periodic solutions for perturbed affine-periodic systems. This kind of affine-periodic solutions has the form of x(t + T) ≡ Qx(t) with some nonsingular matrix Q, which may be quasi-periodic when Q is an orthogonal matrix. It can be even unbounded but \(\frac{{x(t)}}{{|x(t)|}}\) is quasi-periodic, like a helical line, for example x(t) = eat(cosωt, sinωt), when Q is not an orthogonal matrix. The averaging method of higher order for finding affine-periodic solutions is given by topological degree.
Keywords:
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