论文标题
双曲线图轨道测定的渐近行为
Asymptotic behaviour of orbit determination for hyperbolic maps
论文作者
论文摘要
我们处理双曲线图的轨道确定问题。该问题在于确定轨道的初始条件，并最终从某些观察结果中确定模型的其他参数。在同时增加观测值的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。更确切地说，我们描述了解决方案的置信区域的几何形状，从而区分了参数是否添加到初始条件的估计中。我们证明，包含动力学参数会导致不确定性衰减率的变化，如某些已知的数值证据所暗示的那样。
We deal with the orbit determination problem for hyperbolic maps. The problem consists in determining the initial conditions of an orbit and, eventually, other parameters of the model from some observations. We study the behaviour of the confidence region in the case of 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 the solution, distinguishing whether a parameter is added to the estimate of the initial conditions or not. We prove that the inclusion of a dynamical parameter causes a change in the rate of decay of the uncertainties, as suggested by some known numerical evidences.
