1998/01/15 by Saeed Zakeri, Zakeri, Saeed · 1 citation
Mathematics · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions
paper · pdf · doi:10.48550/arxiv.math/9801150
openalex publication_date 1998/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let f be a quadratic polynomial which has an irrationally indifferent fixed point α. Let z be a biaccessible point in the Julia set of f. Then: 1. In the Siegel case, the orbit of z must eventually hit the critical point of f. 2. In the Cremer case, the orbit of z must eventually hit the fixed point α. Siegel polynomials with biaccessible critical point certainly exist, but in the Cremer case it is possible that biaccessible points can never exist. As a corollary, we conclude that the set of biaccessible points in the Julia set of a Siegel or Cremer quadratic polynomial has Brolin measure zero.