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arXiv:math/0609045 [math.DS]AbstractReferencesReviewsResources

A priori bounds for some infinitely renormalizable quadratics: I. Bounded primitive combinatorics

Jeremy Kahn

Published 2006-09-01, updated 2023-12-28Version 3

We prove the a priori bounds for infinitely renormalizable quadratic polynomials for which we can find an infinite sequence of primitive renormalizations such that the ratios of the periods of successive renormalizations is bounded. This implies the local connectivity of the Mandelbrot set at the corresponding points.

Comments: LaTeX, 63 pages, 5 figures
Categories: math.DS
Subjects: 37F25, 37F45
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