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Mark Levi : Arnold diffusion in a chain of coupled pendula



A chain of pendula connected by nearest neighbor coupling is a near-- integrable system if the coupling is weak. As a consequence of KAM, for most initial data the energy of each pendulum stays near its initial value for all time. We show that these KAM motions coexist with ``diffusing" motions for which the energy can leak from any pendulum to any other pendulum, and it can do so with a prescribed itinerary. This is joint work with Vadim Kaloshin.

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