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Collet, Eckmann and the bifurcation measure. (arXiv:1705.06114v1 [math.DS])
来源于:arXiv
The moduli space $\mathcal{M}_d$ of degree $d\geq2$ rational maps can
naturally be endowed with a measure $\mu_\mathrm{bif}$ detecting maximal
bifurcations, called the bifurcation measure. We prove that the support of the
bifurcation measure $\mu_\mathrm{bif}$ has positive Lebesgue measure. To do so,
we establish a general sufficient condition for the conjugacy class of a
rational map to belong to the support of $\mu_\mathrm{bif}$ and we exhibit a
large set of Collet-Eckmann rational maps which satisfy this condition. As a
consequence, we get a set of Collet-Eckmann rational maps of positive Lebesgue
measure which are approximated by hyperbolic rational maps. 查看全文>>