Infinite-dimensional Thurston theory and transcendental dynamics Ⅲ: Entire functions with escaping singular orbits in the degenerate case
Abstract
We classify transcendental entire functions that are compositions of a polynomial and the exponential for which all singular values escape on disjoint rays. We focus on the case where the escape is degenerate in the sense that points from different singular orbits are arbitrarily close to each other. As in the general case, we employ an iteration procedure on an infinite-dimensional Teichmüller space, analogously to the Thurston's classical topological characterization of rational functions, but for an infinite set of marked points.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
History and Theory of Mathematics
Advanced Differential Equations and Dynamical Systems
Publication details
- Journal / source
- Discrete and Continuous Dynamical Systems
- Volume
- 57
- Issue
- 0
- Pages
- 1–23
- Publication date
- 1 January 2026