On the Hausdorff dimension of fractal attractors

@article{Grassberger1981OnTH,
  title={On the Hausdorff dimension of fractal attractors},
  author={Peter Grassberger},
  journal={Journal of Statistical Physics},
  year={1981},
  volume={26},
  pages={173-179}
}
  • P. Grassberger
  • Published 1 September 1981
  • Mathematics
  • Journal of Statistical Physics
We consider such mappingsxn+1=F(xn) of an interval into itself for which the attractor is a Cantor set. For the same class of mappings for which the Feigenbaum scaling laws hold, we show that the Hausdorff dimension of the attractor is universally equal toD=0.538 ... 
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