## Preprint ims07-06

Davoud Cheraghi
Combinatorial Rigidity for Some Infinitely Renormalizable Unicritical Polynomials

Abstract: We prove Combinatorial rigidity for infinitely renormalizable unicritical polynomials, \$f_c:z \mapsto z^d+c\$,with a priori bounds and some "combinatorial condition". Combining with \cite{KL2}, this implies local connectivity of the connectedness locus (the "Mandelbrot set" when \$d=2\$) at the corresponding parameter values.
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