... OpN(f):HN→HNitsquantization. The quantization of the classical map A is a unitary map UN(A)of HN.In [10] we introduced Hecke operators, a group of commuting unitarymaps of HN, which commute with UN(A). ... The classical mechanical system is the iteration ofa linear hyperbolic map A ∈ SL(2, Z) of the torus T2= R2/Z2(a “cat map ).The quantum system is given by specifying an integer N, which ... distribution of matrix elements for the quantum cat map By P¨ar Kurlberg and Ze´ev Rudnick MATRIX ELEMENTS FOR QUANTUM CAT MAPS501Lemma 15. Assume that Q(k),Q(l),Q(m),Q(n) ≡...