Rational Misiurewicz maps are rare II

2007/03/11 by Aspenberg, Magnus
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0703306

Abstract

We show that the set of Misiurewicz maps has Lebesgue measure zero in the space of rational functions for any fixed degree greater than or equal to 2 (generalising the earlier version math.DS/0701382).

Related

• Rational Misiurewicz maps are rare
• Semi-hyperbolic maps are rare
• Rational Misiurewicz maps for which the Julia set is not the whole sphere
• Perturbations of rational Misiurewicz maps
• On the Number of Small Points for Rational Maps