Fractal Dimension of Julia Set for Non-analytic Maps
arXiv:cond-mat/9802308 · doi:10.1023/B:JOSS.0000033174.46243.d4
Abstract
The Hausdorff dimensions of the Julia sets for non-analytic maps: f(z) = z^2 + epsilon z^* and f(z) = {z^*}^2 + epsilon are calculated perturbatively for small epsilon. It is shown that Ruelle's formula for Hausdorff dimensions of analytic maps can not be generalized to non-analytic maps.
A small error corrected. 6 pages, 1 figure. Also available at http://www.neci.nj.nec.com/homepages/tang/ . Submitted to J. Stat. Phys