Hyperbolic systems with non-computable basins of attraction

Abstract

In this paper we show that there is an analytic and computable dynamical system with a hyperbolic sink s such that the basin of attraction of s is not computable. As a consequence, the problem of determining basins of attraction for analytic hyperbolic systems is not, in general, algorithmically solvable. 1 Summary of the paper Dynamical systems are… (More)

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