Thomas Gauthier
Published 2013-12-29, updated 2015-04-24Version 3
In the moduli space of degree d polynomials, the set Per\_n(w) of classes [f] for which f admits a cycle of exact period n and multiplier w is known to be an algebraic hypersurface. We prove that, given a complex number w, these hypersurfaces equidistribute towards the bifurcation current as n tends to infinity.
Comments: Modified third section. Some results of Section 3 have been made more precise. Minor errors corrected
Distribution of polynomials with cycles of given multiplier
Equidistribution speed for endomorphisms of projective spaces
Lyapunov exponents and bifurcation current for polynomial-like maps
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