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In 1982, Ball, Marsden, and Slemrod proved an obstruction to thecontrollability of linear dynamics with a bounded bilinear control term. Thisnote presents an example of nonlinear dynamics with respect to the state forwhich this obstruction still holds while the control potential is not bounded.

Obstruction to the billinear control of the Gross-Pitaevskii equation: an example with an unbounded potential