Discrete Mathematics & Theoretical Computer Science, Vol 4, No 2 (2001)

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DMTCS vol 4 no 2 (2001), pp. 351-356

Discrete Mathematics & Theoretical Computer Science


Volume 4 n° 2 (2001), pp. 351-356

author:Pascal Koiran
title:The topological entropy of iterated piecewise affine maps is uncomputable
keywords:topological entropy, piecewise affine functions, saturated linear functions, cellular automata
abstract: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.
reference: Pascal Koiran (2001), The topological entropy of iterated piecewise affine maps is uncomputable, Discrete Mathematics and Theoretical Computer Science 4, pp. 351-356
bibtex:For a corresponding BibTeX entry, please consider our BibTeX-file.
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