# 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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Automatically produced on Sat Dec 22 22:19:22 CET 2001 by ifalk