## Title data

Canci, Jung Kyu ; Troncoso, Sebastian ; Vishkautsan, Solomon:

**Scarcity of finite orbits for rational functions over a number field.**

*In:* Acta Arithmetica.
Vol. 190
(2019)
Issue 3
.
- pp. 221-237.

ISSN 0065-1036

DOI: https://doi.org/10.4064/aa180210-4-12

## Abstract in another language

Let ϕ be an endomorphism of degree d≥2 of the projective line, defined over a number field K. Let S be a finite set of places of K, including the archimedean places, such that ϕ has good reduction outside S. The article presents two main results. The first result is a bound on the number of K-rational preperiodic points of ϕ in terms of the cardinality of S and the degree d of ϕ. This bound is quadratic in d, which is a significant improvement to all previous bounds in terms of d. The second result is that if there is a K-rational periodic point of period at least 2, then there exists a bound on the number of K-rational preperiodic points of ϕ that is linear in d.

## Further data

Item Type: | Article in a journal |
---|---|

Refereed: | Yes |

Keywords: | preperiodic points; periodic; arithmetic dynamics |

Subject classification: | MSC: Primary 37P05, 37P35; Secondary 11D45 |

Institutions of the University: | Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II (Computer Algebra) |

Result of work at the UBT: | Yes |

DDC Subjects: | 500 Science > 510 Mathematics |

Date Deposited: | 27 Oct 2020 13:09 |

Last Modified: | 27 Oct 2020 13:09 |

URI: | https://eref.uni-bayreuth.de/id/eprint/58782 |