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Monodromization method in the theory of almost-periodic equations

Author: A. A. Fedotov
Translated by: the author
Original publication: Algebra i Analiz, tom 25 (2013), nomer 2.
Journal: St. Petersburg Math. J. 25 (2014), 303-325
MSC (2010): Primary 34E05; Secondary 34E10, 34E20
Published electronically: March 12, 2014
MathSciNet review: 3114856
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Abstract: The basic ideas of the monodromization method, i.e., a renormalization approach to the study of one-dimensional two-frequency quasiperiodic equations, as well as the main results obtained with its help, are described.

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Additional Information

A. A. Fedotov
Affiliation: Division of Mathematics and Mathematical Physics, Department of Physics, St. Petersburg State University, Ul′yanovskaya 3, Petrodvorets, St Petersburg 185504, Russia

Keywords: Quasiperiodic Schr\"odinger operator, difference equation, differential equation, monodromy matrix, Bloch solution, renormalization
Received by editor(s): September 20, 2012
Published electronically: March 12, 2014
Additional Notes: Supported by RFBR (grant no. 11-01-00458-a)
Dedicated: Dedicated to the memory of Vladimir Savel’evich Buslaev
Article copyright: © Copyright 2014 American Mathematical Society