We deal with the orbit determination problem for a class of maps of the cylinder generalizing the Chirikov standard map. The problem consists of determining the initial conditions and other parameters of an orbit from some observations. A solution to this problem goes back to Gauss and leads to the least squares method. Since the observations admit errors, the solution comes with a confidence region describing the uncertainty of the solution itself. We study the behavior of the confidence region in the case of a simultaneous increase of the number of observations and the time span over which they are performed. More precisely, we describe the geometry of the confidence region for solutions in regular zones. We prove an estimate of the trend of the uncertainties in a set of positive measure of the phase space, made of invariant curve. Our result gives an analytical proof of some known numerical evidences.

中文翻译：

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标准类地图的轨道确定：规则区域中置信区域的渐近扩展

我们处理了一类推广 Chirikov 标准地图的圆柱体地图的轨道确定问题。该问题包括根据一些观测确定轨道的初始条件和其他参数。这个问题的解决方案可以追溯到高斯并导致最小二乘法。由于观测值承认错误，因此解带有一个置信区域，用于描述解本身的不确定性。我们研究了在观察次数和执行时间跨度同时增加的情况下置信区域的行为。更准确地说，我们描述了规则区域中解决方案的置信区域的几何形状。我们证明了一组由不变曲线构成的相空间正测度中不确定性趋势的估计。