Irrational rotation numbers and unboundedness of solutions of the second order differential equations with asymmetric nonlinearities期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Irrational rotation numbers and unboundedness of solutions of the second order differential equations with asymmetric nonlinearities

Authors:	Zaihong Wang

Institution:	Department of Mathematics, Capital Normal University, Beijing 100037, People's Republic of China

Abstract:	In this paper, we study the dynamics of the mappings $\begin{displaymath}\begin{cases} \theta_1=\theta+2\alpha\pi+\frac{1}{r}\mu_1(\th... ... r_1=r+\mu_2(\theta)+o(1),\quad\quad r\to+\infty, \end{cases}\end{displaymath}$ where $\alpha$ is a irrational rotation number. We prove the existence of orbits that go to infinity in the future or in the past by using the well-known Birkhoff Ergodic Theorem. Applying this conclusion, we deal with the unboundedness of solutions of Liénard equations with asymmetric nonlinearities.

Keywords:	Unboundedness of solution action-angle variable asymmetric nonlinearity

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