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Non-Computable SRB Measures for Computable Logistic Map Parameters

The existence of computable parameter values of the logistic family for which almost every orbit shares one limiting statistical distribution that is nonetheless not Turing-computable, so no numerical method can approximate it.

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Ulam meets Turing: constructing quadratic maps with non-computable SRB measures

In 1946, S. Ulam invented Monte Carlo method, which has since become the standard numerical technique for making statistical predictions for long-term behaviour of dynamical systems. We show that thi…