Abstract
We study ℓ ∞ norms of ℓ 2-normalized eigenfunctions of quantum cat maps. For maps with short quantum periods (constructed by Bonechi and de Biévre in F Bonechi and S De Bièvre (2000, Communications in Mathematical Physics, 211, 659–686)) we show that there exists a sequence of eigenfunctions u with . For general eigenfunctions we show the upper bound . Here the semiclassical parameter is . Our upper bound is analogous to the one proved by Bérard in P Bérard (1977, Mathematische Zeitschrift, 155, 249-276) for compact Riemannian manifolds without conjugate points.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
