Koiran, Pascal The topological entropy of iterated piecewise affine maps is uncomputable. (English) Zbl 1112.37301 Discrete Math. Theor. Comput. Sci. 4, No. 2, 351-356 (2001). Summary: We show that it is impossible to compute (or even to approximate) 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. Cited in 9 Documents MSC: 37B15 Dynamical aspects of cellular automata Keywords:piecewise affine functions; saturated linear functions; cellular automata PDFBibTeX XMLCite \textit{P. Koiran}, Discrete Math. Theor. Comput. Sci. 4, No. 2, 351--356 (2001; Zbl 1112.37301) Full Text: EuDML EMIS