The topological entropy of iterated piecewise affine maps is uncomputable.

Abstract : We show that it is impossible to compute (or even to approximate) the topological entropy of a continuous piecewise affine function in dimension 4. The same result holds for saturated linear functions in unbounded dimension. We ask whether the topological entropy of a piecewise affine function is always a computable real number, and conversely whether every non-negative computable real number can be obtained as the topological entropy of a piecewise affine function. It seems that these two questions are also open for cellular automata.
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Submitted on : Wednesday, April 17, 2019 - 9:10:56 AM
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Pascal Koiran. The topological entropy of iterated piecewise affine maps is uncomputable.. [Research Report] LIP RR-2000-36, Laboratoire de l'informatique du parallélisme. 2000, 2+7p. ⟨hal-02101967⟩

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