Quantitative reducibility of Gevrey quasi-periodic cocycles and its applications. (1st December 2022)

• Record Type: Journal Article
• Authors: Li, Xianzhe
• Is Part Of: Nonlinearity. Volume 35:Number 12(2022)
• Page Start: 6124
• Page End: 6155
• Publication Date: 2022-12-01
• Subjects: Gevrey class -- long range operator -- pure point spectrum -- interval spectrum -- reducibility theory -- spectral gap; 34L40 -- 81Q10 -- 47B36 -- 70K43 -- 37K55; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/ac98ed
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: We establish a quantitative version of strong almost reducibility result for S L ( 2, R ) quasi-periodic cocycle close to a constant in the Gevrey class. We prove that, if the frequency is Diophantine, the long range operator has pure point spectrum with sub-exponentially decaying eigenfunctions for almost all phases; for the one dimensional quasi-periodic Schrödinger operators with small Gevrey potentials, the length of spectral gaps decays sub-exponentially with respect to its labelling; and the spectrum is an interval for discrete Schrödinger operators acting on Z d with small separable potentials.