Invariant curve theorem for quasiperiodic twist mappings and stability of motion in the Fermi-Ulam problem
Invariant curve theorem for quasiperiodic twist mappings and stability of motion in the Fermi-Ulam problem
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DOI：
10.1088/0951-7715/13/4/308
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发表时间：
2000-07
期刊：
影响因子：
1.7
通讯作者：
V. Zharnitsky
中科院分区：
文献类型：
--
作者：
V. Zharnitsky
本文将单调扭定理推广到拟周期情形，并应用于建立质点在两个拟周期运动壁面之间弹性弹跳系统的运动规律。证明了当频率满足丢番图不等式时，质点的速度在时间上是一致有界的。这回答了Levi和Zehnder最近提出的一个问题（1995 SIAM J. Math. Anal. 26 1233-56）。
In this paper the monotonic twist theorem is extended to the quasiperiodic case and applied to establish regularity of motion in a system of a particle bouncing elastically between two quasiperiodically moving walls. It is shown that the velocity of the particle is uniformly bounded in time if the frequencies satisfy a Diophantine inequality. This answers a question recently asked in Levi and Zehnder (1995 SIAM J. Math. Anal. 26 1233-56).