1,257 research outputs found
Collet, Eckmann and the bifurcation measure
The moduli space of degree rational maps can
naturally be endowed with a measure detecting maximal
bifurcations, called the bifurcation measure. We prove that the support of the
bifurcation measure 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 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
- …