Searching for integrable lattice maps using factorization

Abstract

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 (modified and Schwarzian), for this new model we have also verified the "consistency around a cube".

To appear in Journal of Physics A. Some changes in references

References in corpus (3)

• Classification of integrable equations on quad-graphs. The consistency approach
• Lax pair for the Adler (lattice Krichever-Novikov) System
• Integrable lattice equations and their growth properties

Cited by in corpus (17)

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• Poisson structures for lifts and periodic reductions of integrable lattice equations
• Integrable discrete autonomous quad-equations admitting, as generalized symmetries, known five-point differential-difference equations
• Duality for discrete integrable systems II
• Algebraic entropy computations for lattice equations: why initial value problems do matter
• An algebraic method of classification of S-integrable discrete models
• Algebraic entropy of a class of five-point differential-difference equations
• Algebraic entropy for face-centered quad equations
• On the Coprimeness Property of Discrete Systems without the Irreducibility Condition
• Algebraic entropy for algebraic maps
• Degree growth of lattice equations defined on a 3x3 stencil
• Algebraic entropy for systems of quad equations
• Reconstructing a Lattice Equation: a Non-Autonomous Approach to the Hietarinta Equation
• Generating a chain of maps which preserve the same integral as a given map
• A Lax pair of a lattice equation whose entropy vanishes