2025/05/06 by John Erik Fornaess, Fornaess, John Erik, Mi Hu +1
Engineering · Mathematics · #Dynamical Systems (math.DS) #Engineering Technology and Methodologies #FOS: Mathematics #Modeling, Simulation, and Optimization
paper · pdf · doi:10.48550/arxiv.2505.03503
openalex publication_date 2025/05/06 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28
A basic problem in complex dynamics is to understand orbits of holomorphic maps. One problem is to understand the collection of points S in an attracting basin whose forward orbits land exactly on the attracting fixed point. In the paper [13], the second author showed that for holomorphic polynomials in \mathbb C, there is a constant C so that all Kobayashi discs of radius C must intersect this set S. In the paper [15], the second author showed that there are holomorphic skew products in \mathbb C2 where this result fails. The main result of this paper is to show that for a large class of polynomial skew products, this result nevertheless holds.