Capacities of Julia sets of rational functions

For any polynomialp(z)=a ₀ z ⁿ +a|z ^n–1++a _n , a₀0, n2,F is the Julia set and ^* is the equilibrium distribution onF. Hans Brolin^1] proved that (F)>0, andS ^* =F. Up to now, we know nothing about rational functions. The aim of this paper is to discuss the case of rational functions.Project supported by the Science Fund of the Chinese Academy of Sciences.