Combinatorial rigidity for some infinitely renormalizable unicritical polynomials

Details Combinatorial rigidity for some infinitely renormalizable unicritical polynomials Combinatorial rigidity for some infinitely renormalizable unicritical polynomials

2007-12-20

arxiv.org/abs/0712.3490v3

Mathematics

Dynamical Systems

47 Pages; 7 figures; changes in some proofs; Changes in the writing

Scientific paper

We prove combinatorial rigidity of infinitely renormalizable unicritical
polynomials, P_c :z \mapsto z^d+c, with complex c, under the a priori bounds
and a certain "combinatorial condition". This implies the local connectivity of
the connectedness loci (the Mandelbrot set when d = 2) at the corresponding
parameters.

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