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- W2000528800 abstract "We consider an autonomous system in $mathbb R^n$ having a limitcycle $ x_0$ of period $T>0$ which is nondegenerate in a suitablesense, (see Definition 2.1). We then consider the perturbed system obtained by adding tothe autonomous system a $T$-periodic, not necessarilydifferentiable, term whose amplitude tends to $0$ as a smallparameter $varepsilon>0$ tends to $0.$ Assuming the existence of a$T$-periodic solution $x_varepsilon$ of the perturbed system andits convergence to $ x_0$ as $varepsilonto 0$, the paperestablishes the existence of $Delta_varepsilonto 0$ as$varepsilonto 0$ such that $||x_varepsilon(t+Delta_varepsilon)-x_0(t)||levarepsilon M$ for some $M>0$ and any $varepsilon>0$ sufficiently small. This paper completes thework initiated by the authors in [4] and [11].Indeed, in [4] the existence of a family of $T$-periodicsolutions $x_varepsilon$ of the perturbed system considered herewas proved. While in [11] for perturbed systems in$mathbb R^2$ the rate of convergence was investigated by meansof the method considered in this paper." @default.
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- W2000528800 date "2008-01-01" @default.
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- W2000528800 title "On the rate of convergence of periodic solutions in perturbed autonomous systems as the perturbation vanishes" @default.
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- W2000528800 doi "https://doi.org/10.3934/cpaa.2008.7.49" @default.
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