The Chirikov standard map is a prototypical example of a one-parameter family of volume-preserving maps for which one anticipates chaotic behavior on a non-negligible (positive-volume) subset of phase space for a large set of parameters. Rigorous analysis is notoriously difficult and it remains an open question whether this chaotic region, the stochastic sea, has positive Lebesgue measure for any parameter value. Here we study a problem of intermediate difficulty: compositions of standard maps with increasing coefficient. When the coefficients increase to infinity at a sufficiently fast polynomial rate, we obtain a strong law, a central limit theorem, and quantitative mixing estimates for Holder observables. The methods used are not specific to the standard map and apply to a class of compositions of ‘prototypical’ two-dimensional maps with hyperbolicity on ‘most’ of phase space.

中文翻译：

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系数递增的标准图组成的统计性质

Chirikov 标准映射是单参数体积保持映射系列的原型示例，对于该映射，人们预期在大量参数的相空间的不可忽略（正体积）子集上的混沌行为。严格的分析是出了名的困难，这个混沌区域，即随机海，对于任何参数值是否具有正 Lebesgue 测度仍然是一个悬而未决的问题。在这里，我们研究一个中等难度的问题：标准地图的组合具有增加的系数。当系数以足够快的多项式速率增加到无穷大时，我们获得了强定律、中心极限定理和 Holder 可观测量的定量混合估计。