Equidistribution towards the bifurcation current I : Multipliers and degree d polynomials
Dynamical Systems
2015-04-27 v3 Complex Variables
Abstract
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.
Keywords
Cite
@article{arxiv.1312.7554,
title = {Equidistribution towards the bifurcation current I : Multipliers and degree d polynomials},
author = {Thomas Gauthier},
journal= {arXiv preprint arXiv:1312.7554},
year = {2015}
}
Comments
Modified third section. Some results of Section 3 have been made more precise. Minor errors corrected