Epsilon-Distortion Complexity for Cantor Sets

Details Epsilon-Distortion Complexity for Cantor Sets Epsilon-Distortion Complexity for Cantor Sets

2007-05-07

arxiv.org/abs/0705.0895v1

Mathematics

Dynamical Systems

Scientific paper

We define the epsilon-distortion complexity of a set as the shortest program, running on a universal Turing machine, which produces this set at the precision epsilon in the sense of Hausdorff distance. Then, we estimate the epsilon-distortion complexity of various central Cantor sets on the line generated by iterated function systems (IFS's). In particular, the epsilon-distortion complexity of a C^k Cantor set depends, in general, on k and on its box counting dimension, contrarily to Cantor sets generated by polynomial IFS or random affine Cantor sets.

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