2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79291We prove a strong version of quantum ergodicity for linear hyperbolic maps of the torus (``cat maps''). We show that there is a density one sequence of integers so that as N tends to infinity along this sequence, all eigenfunctions of the quantum propagator at inverse Planck constant N are uniformly distributed. A key step in the argument is to show that for a hyperbolic matrix in the modular group, there is a density one sequence of integers N for which its order (or period) modulo N is somewhat larger than the square root of N.32 pagesNumber TheoryChaotic DynamicsMathematical Physics11text