Deformed Neumann model from spinning strings on $\mathrm{(AdS_5\times S^5)}_\eta$

We show that bosonic spinning strings on the $\eta$-deformed $\mathrm{(AdS_5\times S^5)}$ background are naturally described as periodic solutions of a novel finite-dimensional integrable system which can be viewed as a deformation of the celebrated Neumann model. For this deformed model we find the Lax representation and the analogue of the Uhlenbeck integrals.