Epsilon-Distortion Complexity for Cantor Sets

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dc.creatorBonanno, C.
dc.creatorChazottes, J. -R.
dc.creatorCollet, P.
dc.date2007-05-07
dc.date.accessioned2026-07-07T07:59:47Z
dc.date.available2026-07-07T07:59:47Z
dc.descriptionWe 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.
dc.identifierhttps://arxiv.org/abs/0705.0895
dc.identifierhttp://arxiv.org/abs/0705.0895
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/128500
dc.subjectDynamical Systems
dc.subjectComputational Complexity
dc.subjectMetric Geometry
dc.titleEpsilon-Distortion Complexity for Cantor Sets
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