Pinball Dynamics: Unlimited Energy Growth in Switching Hamiltonian Systems
Pinball Dynamics: Unlimited Energy Growth in Switching Hamiltonian Systems
复制标题
弹球动力学：切换哈密顿系统的无限能量增长
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
V. Zharnitsky
中科院分区：
文献类型：
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作者：
M. Arnold;V. Zharnitsky
考虑了在研究非光滑切换哈密顿系统时自然产生的一组不连续辛映射。该族依赖于两个参数，是研究由非线性共振引起的不连续保面积变换的有界和无界行为的典型模型。本文给出了弹球变换特殊情况的映射的一般描述和非平凡无界解的构造。导出了弹球图在大能量极限下的渐近展开式，并用于构造无界解。对于参数的一般值，在大能量限制下，映射的行为类似于Kesten （Acta Arith 1966）先前考虑的另一个映射。
A family of discontinuous symplectic maps arising naturally in the study of nonsmooth switched Hamiltonian systems is considered. This family depends on two parameters and is a canonical model for the study of bounded and unbounded behavior in discontinuous area-preserving transformations due to nonlinear resonances. This paper provides a general description of the map and a construction of nontrivial unbounded solutions for the special case of the pinball transformation. An asymptotic expansion of the pinball map in the limit of large energy is derived and used for the construction of unbounded solutions. For the generic values of the parameters, in the large energy limit, the map behaves similarly to another one considered earlier by Kesten (Acta Arith 1966).