On some issues concerning polynomial cycles

Tadeusz Pezda

Communications in Mathematics (2013)

  • Volume: 21, Issue: 2, page 129-135
  • ISSN: 1804-1388

Abstract

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We consider two issues concerning polynomial cycles. Namely, for a discrete valuation domain R of positive characteristic (for N ≥ 1 ) or for any Dedekind domain R of positive characteristic (but only for N ≥ 2 ), we give a closed formula for a set 𝒞 Y C L ( R , N ) of all possible cycle-lengths for polynomial mappings in R N . Then we give a new property of sets 𝒞 Y C L ( R , 1 ) , which refutes a kind of conjecture posed by W. Narkiewicz.

How to cite

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Pezda, Tadeusz. "On some issues concerning polynomial cycles." Communications in Mathematics 21.2 (2013): 129-135. <http://eudml.org/doc/260772>.

@article{Pezda2013,
abstract = {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 $\{\mathcal \{C\}YCL\}(R,N)$ of all possible cycle-lengths for polynomial mappings in $R^N$. Then we give a new property of sets $\{\mathcal \{C\}YCL\}(R,1)$, which refutes a kind of conjecture posed by W. Narkiewicz.},
author = {Pezda, Tadeusz},
journal = {Communications in Mathematics},
keywords = {polynomial cycles; discrete valuation domains; Dedekind rings; periodic point; cycle length; polynomial cycles; Dedekind domain; discrete valuation domain},
language = {eng},
number = {2},
pages = {129-135},
publisher = {University of Ostrava},
title = {On some issues concerning polynomial cycles},
url = {http://eudml.org/doc/260772},
volume = {21},
year = {2013},
}

TY - JOUR
AU - Pezda, Tadeusz
TI - On some issues concerning polynomial cycles
JO - Communications in Mathematics
PY - 2013
PB - University of Ostrava
VL - 21
IS - 2
SP - 129
EP - 135
AB - 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 ${\mathcal {C}YCL}(R,N)$ of all possible cycle-lengths for polynomial mappings in $R^N$. Then we give a new property of sets ${\mathcal {C}YCL}(R,1)$, which refutes a kind of conjecture posed by W. Narkiewicz.
LA - eng
KW - polynomial cycles; discrete valuation domains; Dedekind rings; periodic point; cycle length; polynomial cycles; Dedekind domain; discrete valuation domain
UR - http://eudml.org/doc/260772
ER -

References

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  1. Narkiewicz, W., Polynomial Mappings, Lecture Notes in Mathematics, vol. 1600, 1995, Springer-Verlag, Berlin. (1995) MR1367962
  2. Pezda, T., 10.4064/aa108-2-4, Acta Arith., 108, 2, 2003, 127-146. (2003) Zbl1020.11066MR1974518DOI10.4064/aa108-2-4
  3. Pezda, T., 10.1007/s00605-004-0290-z, Monatsh. Math., 145, 2005, 321-331. (2005) Zbl1197.37143MR2162350DOI10.1007/s00605-004-0290-z
  4. Silverman, J.H., 10.1007/978-0-387-69904-2_5, 2007, Springer-Verlag. (2007) MR2316407DOI10.1007/978-0-387-69904-2_5
  5. Zieve, M., Cycles of Polynomial Mappings, PhD thesis, 1996, University of California at Berkeley. (1996) MR2694837

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