| Title:
|
On some issues concerning polynomial cycles (English) |
| Author:
|
Pezda, Tadeusz |
| Language:
|
English |
| Journal:
|
Communications in Mathematics |
| ISSN:
|
1804-1388 |
| Volume:
|
21 |
| Issue:
|
2 |
| Year:
|
2013 |
| Pages:
|
129-135 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider two issues concerning polynomial cycles. Namely, for a discrete valuation domain $R$ of positive characteristic (for $N\ge 1$) or for any Dedekind domain $R$ of positive characteristic (but only for $N\ge 2$), we give a closed formula for a set ${\cal CYCL}(R,N)$ of all possible cycle-lengths for polynomial mappings in $R^N$. Then we give a new property of sets ${\cal CYCL}(R,1)$, which refutes a kind of conjecture posed by W. Narkiewicz. (English) |
| Keyword:
|
polynomial cycles |
| Keyword:
|
discrete valuation domains |
| Keyword:
|
Dedekind rings |
| MSC:
|
11R09 |
| MSC:
|
13F05 |
| MSC:
|
37P35 |
| idZBL:
|
Zbl 06296533 |
| idMR:
|
MR3159285 |
| . |
| Date available:
|
2014-01-27T12:41:41Z |
| Last updated:
|
2014-07-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143586 |
| . |
| Reference:
|
[1] Narkiewicz, W.: Polynomial Mappings, Lecture Notes in Mathematics, vol. 1600.1995, Springer-Verlag, Berlin. MR 1367962 |
| Reference:
|
[2] Pezda, T.: Cycles of polynomial mappings in several variables over rings of integers in finite extensions of the rationals.Acta Arith., 108, 2, 2003, 127-146. Zbl 1020.11066, MR 1974518, 10.4064/aa108-2-4 |
| Reference:
|
[3] Pezda, T.: Cycles of polynomial mappings in several variables over rings of integers in finite extensions of the rationals, II.Monatsh. Math., 145, 2005, 321-331. Zbl 1197.37143, MR 2162350, 10.1007/s00605-004-0290-z |
| Reference:
|
[4] Silverman, J.H.: The Arithmetic of Dynamical Systems, Graduate Texts in Mathematics, No. 241.2007, Springer-Verlag. MR 2316407, 10.1007/978-0-387-69904-2_5 |
| Reference:
|
[5] Zieve, M.: Cycles of Polynomial Mappings.PhD thesis, 1996, University of California at Berkeley. MR 2694837 |
| . |
