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Quadratic polynomials, multipliers and equidistribution | | Xavier Buff
; Thomas Gauthier
; | | Date: |
12 Jun 2013 | | Abstract: | Given a sequence of complex numbers {
ho}_n, we study the asymptotic
distribution of the sets of parameters c {epsilon} C such that the quadratic
maps z^2 +c has a cycle of period n and multiplier {
ho}_n. Assume
1/n.log|{
ho}_n| tends to L. If L {leq} log 2, they equidistribute on the
boundary of the Mandelbrot set. If L > log 2 they equidistribute on the
equipotential of the Mandelbrot set of level 2L - 2 log 2. | | Source: | arXiv, 1306.2736 | | Services: | Forum | Review | PDF | Favorites | |
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