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Density of positive Lyapunov exponents for symplectic cocycles
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2019 (English)In: Journal of the European Mathematical Society (Print), ISSN 1435-9855, E-ISSN 1435-9863, Vol. 21, no 10, p. 3143-3190Article in journal (Refereed) Published
Abstract [en]

We prove that Sp(2d, R)-cocycles, HSp(2d)-cocycles and pseudo-unitary cocycles with at least one non-zero Lyapunov exponent are dense in all usual regularity classes for non-periodic dynamical systems. For Schrodinger operators on the strip, we prove a similar result about the density of positive Lyapunov exponents. This generalizes a result of A. Avila [2] to higher dimensions.

Place, publisher, year, edition, pages
European Mathematical Society Publishing House, 2019. Vol. 21, no 10, p. 3143-3190
Keywords [en]
Lyapunov exponents, Schrodinger operator on strips, symplectic cocycles, Kotani theory, monotonic cocycles, Hermitian symmetric spaces, Siegel upper half-plane, Shilov boundary, Lagrangian Grassmannian
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-257469DOI: 10.4171/JEMS/899ISI: 000480413600005Scopus ID: 2-s2.0-85072680040OAI: oai:DiVA.org:kth-257469DiVA, id: diva2:1347085
Note

QC 20190830

Available from: 2019-08-30 Created: 2019-08-30 Last updated: 2019-10-04Bibliographically approved

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