Initial values problems for lattice equations, and integrability of periodic reductions of integrable cases
I will describe geometrically a way of constructing initial values problems for lattice equations dened on arbitrary stencils. These also provide normal forms for dierence elimination algorithms. By imposing a periodicity condition, the initial value problems yield mappings, or correspondences. If the lattice equation is integrable one expects the periodic reductions to be integrable as well. In a general setting, a lax pair for a lattice equation can be used to construct integrals for the derived mappings. And we can show certain characteristics to grow polynomially as opposed to exponentially for non-integrable systems.