On certain families of rational functions arising in dynamics

In the last decade, it has become apparent that linear systems, depending on parameters, can occur in surprisingly diverse situations, including families of rational solutions to the Korteweg-de Vries equation or to the finite Toda lattice. Now, it turns out that the "inverse scattering" method employed by Moser [12] to obtain canonical coordinates for the finite, homogeneous Toda lattice is precisely the network synthesis question for RC networks, with parameters. The corresponding question has a negative answer in the multivariable RC or for RLC network synthesis, due to global topological obstructions. The multivariable RC setting is ideal for the analysis of the periodic Toda lattice and the topological obstructions are, in fact, generated by tori.