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arxiv: 1306.2736 · v1 · pith:K5WH3423new · submitted 2013-06-12 · 🧮 math.DS · math.CV

Quadratic polynomials, multipliers and equidistribution

classification 🧮 math.DS math.CV
keywords equidistributemandelbrotquadratictheyassumeasymptoticboundarycomplex
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Given a sequence of complex numbers {\rho}_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 {\rho}_n. Assume 1/n.log|{\rho}_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.

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