2009/04/08 by Magnus Aspenberg, Aspenberg, Magnus
Economics, Econometrics and Finance · Mathematics · #Complex Systems and Time Series Analysis #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #math.DS
paper · pdf · doi:10.48550/arxiv.0904.1357
9 pages, 1 figure
arxiv created 2009/04/08 · openalex publication_date 2009/04/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Yoccoz puzzle is a fundamental tool in Holomorphic Dynamics. The original combinatorial argument by Yoccoz, based on the Branner-Hubbard tableau, counts the preimages of a non-degenerate annulus in the puzzle. However, in some important new applications of the puzzle (notably, matings of quadratic polynomials) there is no non-degenerate annulus. We develop a general combinatorial argument to handle this situation. It allows to derive corollaries, such as the local connectedness of the Julia set, for suitable families of rational maps.