可计算性、不可计算性和双曲系统
Computability, Noncomputability, and Hyperbolic Systems
摘要：
本文研究双曲型平衡点的稳定流形和非稳定流形的可计算性。这些流形是表征双曲系统的基本特征。我们证明了（i）这些流形可以局部计算，但（ii）它们不能全局计算（尽管我们证明它们是半可计算的）。我们还表明，Smale的马蹄铁，第一个例子的双曲不变集，既不是一个平衡点，也不是一个周期轨道，是可计算的。
英文摘要：
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.
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