Julia sets are uniformly perfect
AUTOR(ES)
Mane, Ricardo
DATA DE PUBLICAÇÃO
2011
RESUMO
We prove that Julia sets are uniformly perfect in the sense of Pommerenke (Arch. Math. 32 (1979), 192-199). This implies that their linear density of logarithmic capacity is strictly positive, thus implying that Julia sets are regular in the sense of Dirichlet. Using this we obtain a formula for the entropy of invariant harmonic measures on Julia sets. As a corollary we give a very short proof of Lopes converse to Brolin's theorem.
ASSUNTO(S)
teoria ergódica entropia : medidas harmonicas conjuntos de julia
