Monodromization method in the theory of almost-periodic equations

DOI10.1090/S1061-0022-2014-01292-7zbMath1326.39011OpenAlexW2122147402MaRDI QIDQ2930922

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Publication date: 20 November 2014

Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s1061-0022-2014-01292-7

zbMATH Keywords

differential equationmonodromy matrixrenormalizationdifference equationBloch solutionquasiperiodic Schrödinger operator

Mathematics Subject Classification ID

Almost periodic solutions of difference equations (39A24)

Related Items (15)

On the spectrum of a non-self-adjoint quasiperiodic operator ⋮ Complex WKB method for a system of two linear difference equations ⋮ Monodromization and a \(\mathcal{PT}\)-symmetric nonself-adjoint quasi-periodic operator ⋮ Close turning points and the Harper operator ⋮ On \(SL(2,\mathbb{R})\)-cocycles over irrational rotations with secondary collisions ⋮ Complex WKB method (one-dimensional linear problems on the complex plane) ⋮ On Bloch solutions of difference Schrödinger equations ⋮ Semiclassical asymptotics of transition matrices for difference equations with two coalescing turning points ⋮ On the hierarchical behavior of solutions of the Maryland equation in the semiclassical approximation ⋮ Universal hierarchical structure of quasiperiodic eigenfunctions ⋮ An exact renormalization formula for the Maryland model ⋮ Semiclassical asymptotics for a difference Schrödinger equation with two coalescent turning points ⋮ WKB asymptotics of meromorphic solutions to difference equations ⋮ The Complex WKB Method for Difference Equations and Airy Functions ⋮ Difference equations in the complex plane: quasiclassical asymptotics and Berry phase

Cites Work

• Adiabatic almost-periodic Schrödinger operators
• Complex WKB method for adiabatic perturbations of a periodic Schrödinger operator
• On the singular spectrum for adiabatic quasi-periodic Schrödinger operators on the real line
• Une méthode pour minorer les exposants de Lyapounov et quelques exemples montrant le caractère local d'un théorème d'Arnold et de Moser sur le tore de dimension 2
• Positive Lyapunov exponents for Schrödinger operators with quasi- periodic potentials
• Anderson transitions for a family of almost periodic Schrödinger equations in the adiabatic case
• On the difference equations with periodic coefficients
• Analyse semi-classique pour l'équation de Harper (avec application à l'équation de Schrödinger avec champ magnétique)
• Strong resonant tunneling, level repulsion and spectral type for one-dimensional adiabatic quasi-periodic Schrödinger operators
• Weakly resonant tunneling interactions for adiabatic quasi-periodic Schrödinger operators
• Pointwise existence of the Lyapunov exponent for a quasi-periodic equation
• Imaginary parts of Stark–Wannier resonances
• On the absolutely continuous spectrum of one-dimensional quasi-periodic Schrödinger operators in the adiabatic limit
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