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 T² in the semiclassical limit (or equivalently that each semiclassical measure is fully supported on T²). We adapt the proof of a similar result proved for the eigenstates of -Δg on compact hyperbolic surfaces from [arXiv:1705.05019], relying on the fractal uncertainty principle in [arXiv:1612.09040].