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Center for Nonlinear Studies |
We show how to extend classical mechanics into the complex domain. Particles obeying the Heisenberg equations of motion are allowed to move through the complex plane and even to visit many sheets of a Riemann surface. Remarkably rich and beautiful phenomena are discovered, including highly structured classical trajectories that exhibit critical behavior. We also study the complex extension of classical nonlinear wave equations such as the Korteweg-de Vries equation.