类标准映射的轨道确定：规则区域中置信域的渐近展开
Orbit determination for standard-like maps: asymptotic expansion of the confidence region in regular zones
摘要：
本文研究了一类推广了Chirikov标准映射的圆柱映射的定轨问题。该问题包括从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。由于观测值允许误差，因此解带有一个描述解本身不确定性的置信区域。我们研究的行为的置信区域的情况下，同时增加的观察和时间跨度，它们被执行。更确切地说，我们描述的几何形状的置信区域的解决方案，在常规区。我们证明了一个估计的趋势的不确定性的相空间的一组正测度，不变曲线。我们的结果给出了一些已知的数值证据的分析证明。
英文摘要：
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.
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