# American Institute of Mathematical Sciences

December  2006, 16(4): 897-922. doi: 10.3934/dcds.2006.16.897

## Self-similarity of the Mandelbrot set for real essentially bounded combinatorics

Received  September 2005 Revised  July 2006 Published  September 2006

Let us consider a real quadratic-like germ $f_$∗ which is infinitely renormalizable with tripling essentially bounded combinatorics and consider the lamination given by the hybrid classes in the space of quadratic-like germs, then its holonomy map is shown to be $C^1$ at $f_$∗ if the combinatorics of $f_$∗ satisfies a growth condition. As a consequence, a proof of the self-similarity of the Mandelbrot set for this type of combinatorics is given.
Citation: Rogelio Valdez. Self-similarity of the Mandelbrot set for real essentially bounded combinatorics. Discrete & Continuous Dynamical Systems, 2006, 16 (4) : 897-922. doi: 10.3934/dcds.2006.16.897
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