Epsilon-Distortion Complexity for Cantor Sets
Dynamical Systems
2007-05-23 v1 Computational Complexity
Metric Geometry
Abstract
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.
Cite
@article{arxiv.0705.0895,
title = {Epsilon-Distortion Complexity for Cantor Sets},
author = {C. Bonanno and J. -R. Chazottes and P. Collet},
journal= {arXiv preprint arXiv:0705.0895},
year = {2007}
}