at Google ScholarTitle 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) Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics |
| 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 |