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Friction Causing Unpredictability

The periodic motion of a classical point particle in a one-dimensional double-well potential acquires a surprising degree of complexity if friction is added. Finite uncertainty in the initial state can make it impossible to predict in which of the two wells the particle will finally settle. For two models of friction, we exhibit the structure of the basins of attraction in phase space which causes the final-state sensitivity. Adding friction to an integrable system with more than one stable equilibrium emerges as a possible "route to chaos" whenever initial conditions can be specified with finite accuracy only.