Portraits of quadratic rational maps with a small critical cycle
Saved in:
| Title: | Portraits of quadratic rational maps with a small critical cycle |
|---|---|
| Authors: | Tyler Dunaisky, David Krumm |
| Source: | Journal of Number Theory. 275:135-159 |
| Publication Status: | Preprint |
| Publisher Information: | Elsevier BV, 2025. |
| Publication Year: | 2025 |
| Subject Terms: | Mathematics - Number Theory, FOS: Mathematics, Dynamical Systems (math.DS), Number Theory (math.NT), Mathematics - Dynamical Systems, 37P05, 11G30 |
| Description: | Motivated by a uniform boundedness conjecture of Morton and Silverman, we study the graphs of pre-periodic points for maps in three families of dynamical systems, namely the collections of rational functions of degree two having a periodic critical point of period $n$, where $n\in\{2,3,4\}$. In particular, we provide a conjecturally complete list of possible graphs of rational pre-periodic points in the case $n=4$, analogous to well-known work of Poonen for $n=1$, and we strengthen earlier results of Canci and Vishkautsan for $n\in\{2,3\}$. In addition, we address the problem of determining the representability of a given graph in our list by infinitely many distinct linear conjugacy classes of maps. |
| Document Type: | Article |
| Language: | English |
| ISSN: | 0022-314X |
| DOI: | 10.1016/j.jnt.2024.12.008 |
| DOI: | 10.48550/arxiv.2404.00731 |
| Access URL: | http://arxiv.org/abs/2404.00731 |
| Rights: | Elsevier TDM arXiv Non-Exclusive Distribution |
| Accession Number: | edsair.doi.dedup.....bf1b5efb5ee01018b1e8046a490e239b |
| Database: | OpenAIRE |
Full Text Finder 
Nájsť tento článok vo Web of Science | Abstract: | Motivated by a uniform boundedness conjecture of Morton and Silverman, we study the graphs of pre-periodic points for maps in three families of dynamical systems, namely the collections of rational functions of degree two having a periodic critical point of period $n$, where $n\in\{2,3,4\}$. In particular, we provide a conjecturally complete list of possible graphs of rational pre-periodic points in the case $n=4$, analogous to well-known work of Poonen for $n=1$, and we strengthen earlier results of Canci and Vishkautsan for $n\in\{2,3\}$. In addition, we address the problem of determining the representability of a given graph in our list by infinitely many distinct linear conjugacy classes of maps. |
|---|---|
| ISSN: | 0022314X |
| DOI: | 10.1016/j.jnt.2024.12.008 |