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Growth of degrees of integrable mappings
journal contributionposted on 29.03.2022, 05:24 by Pieter Van Der KampPieter Van Der Kamp
We study mappings obtained as s-periodic reductions of the lattice Korteweg-de Vries equation. For small, s ∈ℕ 2we establish upper bounds on the growth of the degree of the numerator of their iterates. These upper bounds appear to be exact. Moreover, we conjecture that for any s 1, s 2 that are co-prime, the growth is, ~(2s 1s 2) -1 n 2except when, s 1+s 2=4 where the growth is linear ~n. Also, we conjecture the degree of the nth iterate in projective space to be ~(s 1+s 2)(2s 1s 2) -1 n 2.