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Initial values problems for lattice equations, and integrability of periodic reductions of integrable cases

van der Kamp, P (La Trobe)
Monday 30 March 2009, 15:30-16:15



I will describe geometrically a way of constructing initial values problems for lattice equations de ned on arbitrary stencils. These also provide normal forms for di erence 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.


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