Searching for integrable lattice maps using factorization

Jarmo Hietarinta, Claude Viallet
2007 Journal of Physics A: Mathematical and Theoretical  
We analyze the factorization process for lattice maps, searching for integrable cases. The maps were assumed to be at most quadratic in the dependent variables, and we required minimal factorization (one linear factor) after 2 steps of iteration. The results were then classified using algebraic entropy. Some new models with polynomial growth (strongly associated with integrability) were found. One of them is a nonsymmetric generalization of the homogeneous quadratic maps associated with KdV
more » ... ciated with KdV (modified and Schwarzian), for this new model we have also verified the "consistency around a cube".
doi:10.1088/1751-8113/40/42/s09 fatcat:f2vstlbn2fe5nlq7nlzikln3zy