Twist Character of the Fourth Order Resonant Periodic Solution |
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| Authors: | Jinzhi?Lei mailto:jzlei@mail.tsinghua.edu.cn" title=" jzlei@mail.tsinghua.edu.cn" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author,Pedro?J.?Torres,Meirong?Zhang |
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| Affiliation: | (1) Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing, 100084, China;(2) Departamento de Matemática Aplicada, Universidad de Granada, 18071 Granada, Spain;(3) Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China |
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| Abstract: | ![]()
In this paper, we will give, for the periodic solution of the scalar Newtonian equation, some twist criteria which can deal with the fourth order resonant case. These are established by developing some new estimates for the periodic solution of the Ermakov–Pinney equation, for which the associated Hill equation may across the fourth order resonances. As a concrete example, the least amplitude periodic solution of the forced pendulum is proved to be twist even when the frequency acroses the fourth order resonances. This improves the results in Lei et al. (2003). Twist character of the least amplitude periodic solution of the forced pendulm. SIAM J. Math. Anal. 35, 844–867.Dedicated to Professor Shui-Nee Chow on the occasion of his 60th birthday. |
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| Keywords: | Twist character periodic solution fourth order resonance third order approximation forced pendulum |
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