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Growth of degrees of lattice equations and its signitures over finite fields

Hold Date
2017-01-18 16:30〜2017-01-18 17:30
Seminar Room W1-C-716, West Zone 1, Ito campus, Kyushu University
Object person
Dinh Tran (University of New South Wales, Australia)

We study growth of degrees of  autonomous and non-autonomous lattice equations, some of which are known to be integrable. We present a conjecture that helps  us to prove polynomial growth  of a  certain class of equations including $Q_V$ and its non-autonomous generalization. In addition, we also study growth of degrees of several non-integrable equations. Exponential growth of degrees of these equations is also proved subject to a conjecture. Our technique is to determine the ambient degree growth of the equations and a conjectured growth of their common factors at each vertex, allowing the true degree growth to be found. Moreover, our results can also be used for mappings obtained as periodic  reductions of integrable lattice equations. We also study signitures of growth of degrees of lattice equations over finite fields. We propose some growth diagnostics over finite fields that can often distinguish between integrable equations and their non-integrable perturbations.