Dynamics of the quasi-periodic Schrodinger cocycle at the lowest energy in the spectrum
2007 (English)In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 272, no 2, 397-442 p.Article in journal (Refereed) Published
In this paper we consider the quasi-periodic Schrodinger cocycle over T-d (d >= 1) and, in particular, its projectivization. In the regime of large coupling constants and Diophantine frequencies, we give an affirmative answer to a question posed by M. Herman [21, p.482] concerning the geometric structure of certain Strange Nonchaotic Attractors which appear in the projective dynamical system. We also show that for some phase, the lowest energy in the spectrum of the associated Schrodinger operator is an eigenvalue with an exponentially decaying eigenfunction. This generalizes  to the multi-frequency case (d > 1).
Place, publisher, year, edition, pages
2007. Vol. 272, no 2, 397-442 p.
anderson localization, integrated density, lyapunov exponents, rotation number, t-d, operators, equations, continuity, potentials, attractors
IdentifiersURN: urn:nbn:se:kth:diva-16787ISI: 000247964500003OAI: oai:DiVA.org:kth-16787DiVA: diva2:334830
QC 201005252010-08-052010-08-05Bibliographically approved