ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

9. Ordinary Differential Equations and Dynamical Systems

1991 MS Classification: 30 Sugawa, Toshiyuki, Kyoto University, Japan An explicit bound for uniform perfectness of Julia sets A compact set C in the Riemann sphere is called uniformly perfect if the moduli of those annuli in the complement which separate C are bounded by some constant M. Mañé-da Rocha and Hinkkanen proved that the Julia set of a rational map of degree ≥ 2 is uniformly perfect, but their proofs seem to provide no explicit bounds. In this talk, an explicit bound M for uniform perfectness will be given in terms of hyperbolic geometry of the Fatou set. As the simplest case, quadratic polynomials will be discussed in more detail.