Mating parabolic rational maps with Hecke groups
Abstract
Abstract We prove that any degree rational map having a parabolic fixed point of multiplier 1 with a fully invariant and simply connected immediate basin of attraction is mateable with the Hecke group , with the mating realised by an algebraic correspondence. This confirms the parabolic version of a conjecture on mateability between rational maps and Hecke groups made by Bullett and Freiberger [Int. J. Mod. Phys. B 17 (2003), 3922–3931]. The proof is in two steps. The first is the construction of a pinched polynomial‐like map which is a mating between a parabolic rational map and a parabolic circle map associated to the Hecke group. The second is lifting this pinched polynomial‐like map to an algebraic correspondence via a suitable branched covering.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Advanced Algebra and Geometry
advanced mathematical theories
Publication details
- Journal / source
- Proceedings of the London Mathematical Society
- Publisher
- Wiley
- Volume
- 132
- Issue
- 3
- Publication date
- 1 March 2026
- Language
- EN