Homeomorphism groups of basilica, rabbit and airplane Julia sets
Abstract
The airplane, the basilica and the Douady rabbit (and, more generally, rabbits with more than two ears) are well-known Julia sets of complex quadratic polynomials. In this paper we study the groups of all homeomorphisms of such fractals and of all automorphisms of their laminations. In particular, we identify them with some kaleidoscopic groups or universal groups and thus realize them as Polish permutation groups. From these identifications, we deduce algebraic, topological and geometric properties of these groups.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Mathematics and Applications
Meromorphic and Entire Functions
Publication details
- Journal / source
- Journal de l’École polytechnique — Mathématiques
- Volume
- 13
- Pages
- 255–320
- Publication date
- 2 February 2026
- Language
- EN