Multipliers of periodic orbits of quadratic polynomials and the parameter plane

Genadi Levin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

We prove a result about an extension of the multiplier of an attracting periodic orbit of a quadratic map as a function of the parameter. This has applications to the problem of geometry of the Mandelbrot and Julia sets. In particular, we prove that the size of p/q-limb of a hyperbolic component of the Mandelbrot set of period n is O(4 n /p), and give an explicit condition on internal arguments under which the Julia set of corresponding (unique) infinitely renormalizable quadratic polynomial is not locally connected.

Original languageAmerican English
Pages (from-to)285-315
Number of pages31
JournalIsrael Journal of Mathematics
Volume170
Issue number1
DOIs
StatePublished - Mar 2009

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