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We give an explicit construction of all quasicircles, modulo bilipschitz maps. More precisely, we construct a class of planar Jordan curves, using a process similar to the construction of the van Koch snowflake curve. These snowflake-like curves are easily seen to be quasicircles. We prove that for every quasicircle Γ there is a bilipschitz homeomorphism f of the plane and a snowflake-like curve S ∈ with Γ = f(). In the same fashion we obtain a construction of all bilipschitz-homogeneous Jordan...
We prove that the Julia set of a rational map of the Riemann sphere satisfying the Collet-Eckmann condition and having no parabolic periodic point is mean porous, if it is not the whole sphere. It follows that the Minkowski dimension of the Julia set is less than 2.
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