Classification theory for higher-rank mappings

Develop a general classification theory for higher-rank rational discrete mappings, including a framework to construct spaces of initial conditions and to compute degree growth and algebraic entropy.

Background

Rank-2 mappings have a well-developed algebro-geometric theory linking spaces of initial conditions to algebraic entropy, but such a comprehensive theory does not exist for higher-rank mappings. The authors explicitly highlight this gap while positioning their work on lattice equations.