Computability, Noncomputability, and Hyperbolic Systems
Logic
2016-11-26 v1
Abstract
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.
Cite
@article{arxiv.1201.0164,
title = {Computability, Noncomputability, and Hyperbolic Systems},
author = {Daniel S. Graca and Ning Zhong and Jorge Buescu},
journal= {arXiv preprint arXiv:1201.0164},
year = {2016}
}