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 in 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.

我们处理双曲线地图的轨道确定问题。问题在于确定轨道的初始条件，并最终根据一些观测确定模型的其他参数。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，我们描述了解决方案置信区域的几何形状，区分是否将参数添加到初始条件的估计中。我们证明，正如一些已知的数值证据所表明的那样，包含一个动力学参数会导致不确定性衰减率的变化。