| The Topological Entropy of Iterated Piecewise Ane Maps is Uncomputable (2007) | |||||||||||||||||
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| We show that it is impossible to compute (or even to approximate) the topological entropy of a continuous piecewise ane function in dimension 4. The same result holds for saturated linear functions in unbounded dimension. We ask whether the topological entropy of a piecewise ane 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 ane function. It seems that these two questions are also open for cellular automata. | |||||||||||||||||
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