Dynamics of some piecewise smooth Fermi-Ulam models.
Dynamics of some piecewise smooth Fermi-Ulam models.
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DOI：
10.1063/1.3695379
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发表时间：
2011-12
期刊：
影响因子：
2.9
通讯作者：
J. de Simoi;D. Dolgopyat
中科院分区：
文献类型：
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作者：
J. de Simoi;D. Dolgopyat
我们找到了一类分段光滑Fermi-Ulam乒乓模型的规范形，它描述了这类模型的高能动力学。取决于单个真实的参数的值，动力学可以是双曲线的或椭圆的。在第一种情况下，我们证明了费米加速轨道集的测度为零，但具有完整的Hausdorff维数。我们还表明，几乎每一个轨道，能量最终下降到低于一个固定的阈值福尔斯。在第二种情况下，我们证明，一般来说，对于任意高的能量，我们都有稳定的周期轨道，并且费米加速轨道集可能有无限的测度。
We find a normal form which describes the high energy dynamics of a class of piecewise smooth Fermi-Ulam ping pong models. Depending on the value of a single real parameter, the dynamics can be either hyperbolic or elliptic. In the first case, we prove that the set of orbits undergoing Fermi acceleration has zero measure but full Hausdorff dimension. We also show that for almost every orbit, the energy eventually falls below a fixed threshold. In the second case, we prove that, generically, we have stable periodic orbits for arbitrarily high energies and that the set of Fermi accelerating orbits may have infinite measure.