Abstract
The Hausdorff dimensions of the Julia sets for nonanalytic maps f(z) = z 2+εz* and f(z)=z*2+ε are calculated perturbatively for small ε. It is shown that Ruelle's formula for the Hausdorff dimensions of analytic maps cannot be generalized to nonanalytic maps.
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Tang, C. Fractal Dimension of Julia Set for Nonanalytic Maps. Journal of Statistical Physics 93, 1001–1008 (1998). https://doi.org/10.1023/B:JOSS.0000033174.46243.d4
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DOI: https://doi.org/10.1023/B:JOSS.0000033174.46243.d4