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Prevalent behavior of smooth strongly monotone discrete-time dynamical systems
Yi Wang, Jinxiang Yao, Yufeng Zhang
Source abstract
For C 1 C^{1} -smooth strongly monotone discrete-time dynamical systems, it is shown that “convergence to linearly stable cycles” is a prevalent asymptotic behavior in the measure-theoretic sense. The results are then applied to several classes of time-periodic parabolic equations and obtain the prevalence of convergence to periodic solutions.
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