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We prove global attraction to stationary orbits for 3D Dirac equation with concentrated nonlinearity. We show that each finite energy solution converges as    $$t\rightarrow \pm \infty $$  t → ± ∞ to the set of four-frequency “nonlinear eigenfunctions”. The global attraction is caused by nonlinear energy transfer from lower harmonics to the continuous spectrum and subsequent dispersion radiation.

Global attractor for 3D Dirac equation with nonlinear point interaction