Grand orbit relations in wandering domains
One of the fundamental distinctions in McMullen and Sullivan’s description of the Teichmüller space of a complex dynamical system is between discrete and indiscrete grand orbit relations. We investigate these on the Fatou set of transcendental entire maps and provide criteria to distinguish between the two types. Furthermore, we show that discrete and indiscrete grand orbit relations may coexist non-trivially in a wandering domain, a phenomenon which does not occur for any other type of Fatou component. One of the tools used is a novel quasiconformal surgery construction of independent interest.
Authors
- Núria Fagella (ORCID: https://orcid.org/0000-0002-5466-0579)
- Lukáš Geyer (ORCID: https://orcid.org/0000-0001-5889-9037)
- Vasiliki Evdoridou (ORCID: https://orcid.org/0000-0002-5409-2663)
- Leticia Pardo‐Simón (ORCID: https://orcid.org/0000-0003-4039-5556)
Institutions
- The Open University (GB)
- Montana State University (US)
- Centre de Recerca Matemàtica (ES)
- Universitat de Barcelona (ES)
Publication Details
- Journal
- Revista Matemática Iberoamericana
- Published
- 2026-06-19
- DOI
- https://doi.org/10.4171/rmi/1631
- Primary Topic
- Mathematical Dynamics and Fractals
- Type
- preprint
- Field-Weighted Citation Impact
- 0.00
Funders
- Institució Catalana de Recerca i Estudis Avançats
- Agencia Estatal de Investigación