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Some remarks on the dynamics of the almost Mathieu equation at critical coupling*
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2020 (English)In: Nonlinearity, ISSN 0951-7715, E-ISSN 1361-6544, Vol. 33, no 6, p. 2707-2722Article in journal (Refereed) Published
Abstract [en]

We show that the quasi-periodic Schrodinger cocycle with a continuous potential is of parabolic type, with a unique invariant section, at all gap edges where the Lyapunov exponent vanishes. This applies, in particular, to the almost Mathieu equation with critical coupling. It also provides examples of real-analytic cocycles having a unique invariant section which is not smooth.

Place, publisher, year, edition, pages
IOP PUBLISHING LTD , 2020. Vol. 33, no 6, p. 2707-2722
Keywords [en]
quasi-periodic cocycle, almost Mathieu operator, discrete Schrodinger operator
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-273488DOI: 10.1088/1361-6544/ab7636ISI: 000528626500001Scopus ID: 2-s2.0-85085650489OAI: oai:DiVA.org:kth-273488DiVA, id: diva2:1431709
Note

QC 20200525

Available from: 2020-05-25 Created: 2020-05-25 Last updated: 2022-06-26Bibliographically approved

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Bjerklöv, Kristian

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