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Title:
Non-unique trajectories of Hamiltonian vector fields
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Abstract:
We’ll discuss a construction of an autonomous Hamiltonian Sobolev vector field in 4 dimensions such that for a positive measure of initial points, there are at least two trajectories emanating from them. We’ll also see that the Hamiltonian need not be preserved along such trajectories. We use convex integration techniques and the Ambrosio superposition principle in the proof. This is joint work with Massimo Sorella.
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