Epsilon-Distortion Complexity for Cantor Sets

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

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.

Keywords

Dynamical Systems, Computational Complexity, Metric Geometry

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/128500

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0705.0895
 http://arxiv.org/abs/0705.0895

Collections

arXiv