Polynomial maps with a Julia set of positive measure

Abstract

In this paper we shall show that there exists L_0 such that for each even integer L >= L_0 there exists $c_1 \in \rz$ for which the Julia set of $z-->z^L+c_1$ has positive Lebesgue measure. This solves an old problem. Editor's note: In 1997, it was shown by Xavier Buff that there was a serious flaw in the argument, leaving a gap in the proof. Currently (1999), the question of polynomials with a positive measure Julia sets remains open.

References in corpus (8)

• Dynamics in one complex variable: introductory lectures
• On the Lebesgue measure of the Julia set of a quadratic polynomial
• Ergodic theory for smooth one-dimensional dynamical systems
• Hyperbolicity is dense in the real quadratic family
• Combinatorics, geometry and attractors of quasi-quadratic maps
• Quasisymmetric conjugacies between unimodal maps
• Induced expansion for quadratic polynomials
• One-dimensional maps and Poincaré metric

Cited by in corpus (2)

• Limit Drift for Complex Feigenbaum Mappings
• The topological complexity of Cantor attractors for unimodal interval maps