Parameter scaling for the Fibonacci point
Leroy Wenstrom
Abstract
We prove geometric and scaling results for the real Fibonacci parameter value in the quadratic family fc(z) = z2+c. The principal nest of the Yoccoz parapuzzle pieces has rescaled asymptotic geometry equal to the filled-in Julia set of z2-1. The modulus of two such successive parapuzzle pieces increases at a linear rate. Finally, we prove a ``hairiness" theorem for the Mandelbrot set at the Fibonacci point when rescaling at this rate.
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