## Institute for Mathematical Sciences

## Preprint ims96-4

** L. Wenstrom**
* Parameter Scaling for the Fibonacci Point*

Abstract: We prove geometric and scaling results for the real Fibonacci parameter value in the quadratic family $f_c(z) = z^2+c$. The
principal nest of the Yoccoz parapuzzle pieces has rescaled
asymptotic geometry equal to the filled-in Julia set of
$z^2-1$. 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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