Non-uniform Porosity for a Subset of Some Julia Sets.

Published in Contemporary Math Series of the AMS, 2006

Recommended citation: "Non-uniform Porosity for a Subset of Some Julia Sets.", K. A. Roth, Proceedings of Complex Dynamics: 25 years after the first appearance of the Mandelbrot Set, published in the Contemporary Math Series of the AMS, 2006. http://jcsites.juniata.edu/faculty/roth/formalporousarticle.pdf

Using similar techniques to McMullen’s paper, it is shown that the boundary of the basin of infinity of fθ(z) = e2πiτ(θ)z2 (z−3) , called Jθ , is non-uniformly porous for all irrational θ ∈ (0, 1).

Download paper here

Recommended citation: “Non-uniform Porosity for a Subset of Some Julia Sets.”, K. A. Roth, Proceedings of Complex Dynamics: 25 years after the first appearance of the Mandelbrot Set, published in the Contemporary Math Series of the AMS, 2006.