Abstract
We study the eigenfunctions of the quantized cat map, desymmetrized by Hecke operators. In the papers (Olofsson in Ann Henri Poincare 10(6):1111–1139, 2009; Math Phys 286(3):1051–1072, 2009) it was observed that when the inverse of Planck’s constant is a prime exponent N = pn, with n > 2, half of these eigenfunctions become large at some points, and half remains small for all points. In this paper we study the large eigenfunctions more carefully. In particular, we answer the question of for which q the Lq norms remain bounded as N goes to infinity. The answer is q ≤ 4.
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