标题： 可计算性，不可计算性与双曲系统 显示英文标题

标题： Computability, Noncomputability, and Hyperbolic Systems

摘要： 本文研究了双曲平衡点的稳定流形和不稳定流形的可计算性。这些流形是表征双曲系统的本质特征。我们证明了：(i) 局部上可以计算这些流形，但 (ii) 在全局上不能（尽管我们证明它们是半可计算的）。我们还证明了，作为第一个既非平衡点也非周期轨道的双曲不变集的例子，斯梅尔的马蹄是可计算的。 显示英文摘要

摘要： In this paper we study the computability of the stable and unstable manifolds of a hyperbolic equilibrium point. These manifolds are the essential feature which characterizes a hyperbolic system. We show that (i) locally these manifolds can be computed, but (ii) globally they cannot (though we prove they are semi-computable). We also show that Smale's horseshoe, the first example of a hyperbolic invariant set which is neither an equilibrium point nor a periodic orbit, is computable.