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In many applications one is interested in finding the stability regions(basins of attraction) of some stationary states (attractors). In this paper weshow that one cannot compute, in general, the basins of attraction of even veryregular systems, namely analytic systems with hyperbolic asymptotically stableequilibrium points. To prove the main theorems, a new method for embedding adiscrete-time system into a continuous-time system is developed.

An analytic system with a computable hyperbolic sink whose basin of attraction is non-computable