论文标题
标准图的轨道测定：常规区域中置信区的渐近扩张
Orbit determination for standard-like maps: asymptotic expansion of the confidence region in regular zones
论文作者
论文摘要
我们处理概括Chirikov标准地图的圆柱地图的轨道确定问题。该问题包括从某些观测值确定轨道的初始条件和其他参数。解决此问题的解决方案可以追溯到高斯，并导致最小二乘方法。由于观察结果承认错误，该解决方案带有一个置信区，描述了解决方案本身的不确定性。在同时增加观测值数量和执行它们的时间跨度的情况下，我们研究了置信区的行为。更准确地说，我们描述了常规区域中解决方案的置信区域的几何形状。我们证明了在不变曲线制成的一系列积极衡量相空间中不确定性的趋势的估计。我们的结果给出了一些已知数值证据的分析证明。
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.
