We consider the mass-in-mass (MiM) lattice when the internal resonators are very small. When there are no internal resonators the lattice reduces to a standard Fermi-Pasta-Ulam-Tsingou (FPUT) system. We show that the solution of the MiM system, with suitable initial data, shadows the FPUT system for long periods of time. Using some classical oscillatory integral estimates we can conclude that the error of the approximation is (in some settings) higher than one may expect.

中文翻译：

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具有小内部谐振器的质中量晶格

当内部谐振器非常小时，我们考虑质量质量 (MiM) 晶格。当没有内部谐振器时，晶格简化为标准的 Fermi-Pasta-Ulam-Tsingou (FPUT) 系统。我们展示了具有合适初始数据的 MiM 系统的解决方案，可以长时间地影响 FPUT 系统。使用一些经典的振荡积分估计，我们可以得出结论，近似值的误差（在某些设置中）高于预期。