Computability, Noncomputability, and Hyperbolic Systems

Details Computability, Noncomputability, and Hyperbolic Systems Computability, Noncomputability, and Hyperbolic Systems

2011-12-30

arxiv.org/abs/1201.0164v1

Mathematics

Logic

Scientific paper

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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