Algebraic entropy of a multi-term recurrence of the Hietarinta-Viallet type
arXiv:1812.08923
Abstract
We introduce a family of extensions of the Hietarinta-Viallet equation to a multi-term recurrence relation via a reduction from the coprimeness-preserving extension to the discrete KdV equation. The recurrence satisfies the irreducibility and the coprimeness property although it is nonintegrable in terms of an exponential degree growth. We derive the algebraic entropy of the recurrence by an elementary method of calculating the degree growth. The result includes the entropy of the original Hietarinta-Viallet equation.
arXiv comment24 pages, To appear in RIMS Kokyuroku Bessatsu
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