Computability, noncomputability, and hyperbolic systems
Copyright policy )Computability, noncomputability, and hyperbolic systems
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.
- University of Algarve Portugal
- University of Lisbon Portugal
- University of Cincinnati United States
- Instituto de Telecomunicações Portugal
- University System of Ohio United States
computability, Dynamical systems with hyperbolic orbits and sets, Applications of computability and recursion theory, FOS: Mathematics, Mathematics - Logic, Computation over the reals, computable analysis, hyperbolic systems, Logic (math.LO), Smale's horseshoe, Strange attractors, chaotic dynamics of systems with hyperbolic behavior
computability, Dynamical systems with hyperbolic orbits and sets, Applications of computability and recursion theory, FOS: Mathematics, Mathematics - Logic, Computation over the reals, computable analysis, hyperbolic systems, Logic (math.LO), Smale's horseshoe, Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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