Existence of quasiperiodic solutions and Littlewood’s boundedness problem of super-linear impact oscillators
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摘要
So far most application of Kolmogorov–Arnold–Moser (KAM) theory has been restricted to smooth dynamical systems. In this paper, it is shown by a series of transformations that how KAM theory can be used to analyze the dynamical behavior of Duffing-type equations with impact. The analysis is carried out for the example(0.1)x¨+x2n+1=p(t),forx(t)>0,x(t)⩾0,x˙(t0+)=-x˙(t0-),ifx(t0)=0with p ∈ C5 being periodic. We prove that all solutions are bounded, and that there are infinitely many periodic and quasiperiodic solutions in this case.
论文关键词:Impact oscillators,Boundedness of solutions,KAM,Quasiperiodic solutions,Action-angle variables
论文评审过程:Available online 20 January 2011.
论文官网地址:https://doi.org/10.1016/j.amc.2011.01.037