Geodesic
The topological entropy of iterated piecewise affine maps is uncomputable
Discrete mathematics & theoretical computer science, Tome 4 (2000-2001) no. 2.

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We show that it is impossible to compute (or even to approximate) the topological entropy of a continuous piecewise affine function in dimension four. 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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     author = {Koiran, Pascal},
     title = {The topological entropy of iterated piecewise affine maps is uncomputable},
     journal = {Discrete mathematics & theoretical computer science},
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Koiran, Pascal. The topological entropy of iterated piecewise affine maps is uncomputable. Discrete mathematics & theoretical computer science, Tome 4 (2000-2001) no. 2. doi : 10.46298/dmtcs.292. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.292/

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