## Symmetries of Julia sets for rational maps

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- by Gustavo Rodrigues Ferreira
- Conform. Geom. Dyn.
**27**(2023), 145-160 - DOI: https://doi.org/10.1090/ecgd/383
- Published electronically: February 28, 2023
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## Abstract:

Since the 1980s, much progress has been done in completely determining which functions share a Julia set. The polynomial case was completely solved in 1995, and it was shown that the symmetries of the Julia set play a central role in answering this question. The rational case remains open, but it was already shown to be much more complex than the polynomial one. Here, we offer partial extensions to Beardon’s results on the symmetry group of Julia sets, and discuss them in the context of singularly perturbed maps.## References

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## Bibliographic Information

**Gustavo Rodrigues Ferreira**- Affiliation: Institute of Mathematics and Statistics, University of São Paulo, Brazil
- Address at time of publication: Department of Mathematics, Imperial College London, United Kingdom
- MR Author ID: 1479174
- ORCID: 0000-0002-7330-0018
- Email: g.rodrigues-ferreira@imperial.ac.uk
- Received by editor(s): August 19, 2019
- Received by editor(s) in revised form: December 22, 2021, and June 7, 2022
- Published electronically: February 28, 2023
- © Copyright 2023 American Mathematical Society
- Journal: Conform. Geom. Dyn.
**27**(2023), 145-160 - MSC (2020): Primary 37F10
- DOI: https://doi.org/10.1090/ecgd/383
- MathSciNet review: 4553913