The full delocalization of eigenstates for the quantized cat map

We consider the quantum cat map - a toy model of a quantized chaotic system. We show that its eigenstates are fully delocalized on ${\mathbb{T}}^2$ in the semiclassical limit (or equivalently that each semiclassical measure is fully supported on ${\mathbb{T}}^2$). We adapt the proof of a similar result proved for the eigenstates of $-{\mathrm{\Delta }}_g$ on compact hyperbolic surfaces from [arXiv:1705.05019], relying on the fractal uncertainty principle in [arXiv:1612.09040].