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We consider the nonlinear Schrodinger equation, with mass-criticalnonlinearity, focusing or defocusing. For any given angle, we establish theexistence of infinitely many functions on which the scattering operator acts asa rotation of this angle. Using a lens transform, we reduce the problem to theexistence of a solution to a nonlinear Schrodinger equation with harmonicpotential, satisfying suitable periodicity properties. The existence ofinfinitely many such solutions is proved thanks to a constrained minimizationproblem.

Rotating points for the conformal NLS scattering operator