Distribution of postcritically finite polynomials

2013/02/04 by Favre, Charles, Gauthier, Thomas · 1 citation
#Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1302.0810

Abstract

We prove that Misiurewicz parameters with prescribed combinatorics and hyperbolic parameters with (d - 1) distinct attracting cycles with given multipliers are equidistributed with respect to the bifurcation measure in the moduli space of degree d complex polynomials. Our proof relies on Yuan's equidistribution results of points of small heights, and uses in a crucial way Epstein's transversality results.

Cited by

• Iterates of post-critically finite polynomials of the form \boldsymbolx^d+c

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