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An algorithm determining the set of lengths of polynomial cycles in $Z_K^N$

Volume 166 / 2021

Tadeusz Pezda Colloquium Mathematicum 166 (2021), 151-169 MSC: Primary 11R09; Secondary 11S82, 37P35. DOI: 10.4064/cm8188-2-2021 Published online: 28 June 2021


We give a finitary procedure of finding the set of lengths of cycles for polynomial mappings in several variables over discrete valuation domains. As a consequence, we obtain a procedure of determining the set of cycle-lengths of $N\ge 2$ variables over $Z_K$ for any algebraic number field $K$. In our earlier paper, we gave a procedure working for one variable only.


  • Tadeusz PezdaInstitute of Mathematics
    University of Wrocław
    Pl. Grunwaldzki 2/4
    50-384 Wrocław, Poland

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