Growth of degrees of integrable mappings

Details Growth of degrees of integrable mappings Growth of degrees of integrable mappings

2010-05-12

arxiv.org/abs/1005.2065v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

14 pages, submitted to Journal of difference equations and applications

Scientific paper

We study mappings obtained as s-periodic reductions of the lattice Korteweg-De Vries equation. For small s=(s1,s2) we 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 s1,s2 that are co-prime the growth is ~n^2/(2s1s2), except when s1+s2=4 where the growth is linear ~n. Also, we conjecture the degree of the n-th iterate in projective space to be ~n^2(s1+s2)/(2s1s2).

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