We consider the quantum cat map -a toy model of a quantized chaotic system. We show that its eigenstates are fully delocalized on T 2 in the semiclassical limit (or equivalently that each semiclassical measure is fully supported on T 2 ). We adapt the proof of a similar result proved for the eigenstates of −∆ g on compact hyperbolic surfaces from [DJ18], relying on the fractal uncertainty principle in [BD18].
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