Uniform boundedness on rational maps with automorphisms
Abstract
In this paper, we study the dynamical uniform boundedness principle over a family of rational maps with certain nontrivial automorphisms. Specifically, we consider a family of rational maps of an arbitrary degree $d\ge 2$ whose automorphism group contains the cyclic group of order $d$. We prove that a subfamily of this family satisfies the dynamical uniform boundedness principle.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2024
- DOI:
- 10.48550/arXiv.2401.11309
- arXiv:
- arXiv:2401.11309
- Bibcode:
- 2024arXiv240111309H
- Keywords:
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- Mathematics - Number Theory;
- Mathematics - Dynamical Systems;
- 37P05
- E-Print:
- 13 pages