Fractal Dimension of Julia Set for Non-analytic Maps

Details Fractal Dimension of Julia Set for Non-analytic Maps Fractal Dimension of Julia Set for Non-analytic Maps

1998-02-27

arxiv.org/abs/cond-mat/9802308v3

J. Stat. Phys., vol.93, No.3/4, 1001 (1998).

Physics

Condensed Matter

Statistical Mechanics

A small error corrected. 6 pages, 1 figure. Also available at http://www.neci.nj.nec.com/homepages/tang/ . Submitted to J. Sta

Scientific paper

10.1023/B:JOSS.0000033174.46243.

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.

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