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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Irrational rotation numbers and unboundedness of solutions of the second order differential equations with asymmetric nonlinearities
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by Zaihong Wang PDF
Proc. Amer. Math. Soc. 131 (2003), 523-531 Request permission

Abstract:

In this paper, we study the dynamics of the mappings \begin{equation*} \begin {cases} \theta _1=\theta +2\alpha \pi +\frac {1}{r}\mu _1(\theta )+o(r^{-1}), r_1=r+\mu _2(\theta )+o(1),\quad \quad r\to +\infty , \end{cases} \end{equation*} 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.
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Additional Information
  • Zaihong Wang
  • Affiliation: Department of Mathematics, Capital Normal University, Beijing 100037, People’s Republic of China
  • Email: zhwang@mail.cnu.edu.cn
  • Received by editor(s): March 19, 2001
  • Received by editor(s) in revised form: September 22, 2001
  • Published electronically: June 3, 2002
  • Additional Notes: The author’s research was supported by the National Natural Science Foundation of China, No.10001025, and by the Natural Science Foundation of Beijing (1022003)
  • Communicated by: Carmen C. Chicone
  • © Copyright 2002 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 131 (2003), 523-531
  • MSC (2000): Primary 34C25; Secondary 34B15
  • DOI: https://doi.org/10.1090/S0002-9939-02-06601-7
  • MathSciNet review: 1933343