动力系统、模拟、抽象计算
Dynamical systems, simulation, abstract computation
摘要：
我们调查了最近的发展领域，有关动态的理论计算机科学。我们讨论了动力系统中感兴趣的量的模拟和计算的理论极限。我们将集中在动力学理论的中心对象，作为不变测度和不变集，表明即使它们可以在许多有趣的情况下以任意精度计算，也存在一些情况下，它们不能。我们还解释了如何有可能计算遍历平均的收敛速度（当系统是已知的），以及如何这需要计算任意好的近似点的空间具有典型的统计行为（一种建设性版本的逐点遍历定理）。
英文摘要：
We survey an area of recent development, relating dynamics to theoretical computer science. We discuss the theoretical limits of simulation and computation of interesting quantities in dynamical systems. We will focus on central objects of the theory of dynamics, as invariant measures and invariant sets, showing that even if they can be computed with arbitrary precision in many interesting cases, there exists some cases in which they can not. We also explain how it is possible to compute the speed of convergence of ergodic averages (when the system is known exactly) and how this entails the computation of arbitrarily good approximations of points of the space having typical statistical behaviour (a sort of constructive version of the pointwise ergodic theorem).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
