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Large Newforms of the Quantized Cat Map Revisited
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
2010 (English)In: Annales de l'Institute Henri Poincare. Physique theorique, ISSN 1424-0637, E-ISSN 1424-0661, Vol. 11, no 7, 1285-1302 p.Article in journal (Refereed) Published
Abstract [en]

We study the eigenfunctions of the quantized cat map, desymmetrized by Hecke operators. In the papers (Olofsson in Ann Henri Poincar, 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 = p (n) , 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 L (q) norms remain bounded as N goes to infinity. The answer is q a parts per thousand currency sign 4.

Place, publisher, year, edition, pages
2010. Vol. 11, no 7, 1285-1302 p.
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URN: urn:nbn:se:uu:diva-148660DOI: 10.1007/s00023-010-0057-0ISI: 000285783400004OAI: oai:DiVA.org:uu-148660DiVA: diva2:402652
Available from: 2011-03-09 Created: 2011-03-09 Last updated: 2011-03-09Bibliographically approved

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