English

On computational complexity of Siegel Julia sets

Dynamical Systems 2009-11-11 v2 Computational Complexity

Abstract

It has been previously shown by two of the authors that some polynomial Julia sets are algorithmically impossible to draw with arbitrary magnification. On the other hand, for a large class of examples the problem of drawing a picture has polynomial complexity. In this paper we demonstrate the existence of computable quadratic Julia sets whose computational complexity is arbitrarily high.

Keywords

Cite

@article{arxiv.math/0502354,
  title  = {On computational complexity of Siegel Julia sets},
  author = {I. Binder and M. Braverman and M. Yampolsky},
  journal= {arXiv preprint arXiv:math/0502354},
  year   = {2009}
}

Comments

Updated version, to appear in Commun. Math. Phys

R2 v1 2026-07-22T17:15:45.616Z