Directional differentiability of the rotation number for the almost- periodic Schrödinger equation

DOI10.1215/S0012-7094-92-06617-8zbMath0763.34060MaRDI QIDQ1196397

Rafael Obaya, Miguel Paramio

Publication date: 14 December 1992

Published in: Duke Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

differentiabilityone-dimensional Schrödinger equationalmost periodic potentialdirectional differentiability of the rotation numbervariation of the rotation number

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40)

Related Items

Linear invariant measures for recurrent linear systems ⋮ Dynamical description of bidimensional linear systems with a measurable 2-sheet ⋮ Resonance tongues and instability pockets in the quasi-periodic Hill-Schrödinger equation ⋮ Li–Yorke chaos in nonautonomous Hopf bifurcation patterns—I ⋮ On the dynamical behaviour of an almost periodic linear system with an ergodic 2-sheet studied by R. Johnson ⋮ Ergodic properties and rotation number for linear Hamiltonian systems ⋮ An ergodic classification of bidimensional linear systems ⋮ Time averages for continuous functions on distal flows

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An extension of a result by Dinaburg and Sinai on quasi-periodic potentials
• Almost periodic Schrödinger operators. II: The integrated density of states
• Cantor spectrum for the quasi-periodic Schrödinger equation
• Cantor spectrum for the almost Mathieu equation
• The spectrum of a quasiperiodic Schrödinger operator
• The Floquet exponent for two-dimensional linear systems with bounded coefficients
• Spectral properties of disordered systems in the one-body approximation
• An example of a Schrödinger equation with almost periodic potential and nowhere dense spectrum
• The rotation number for almost periodic potentials
• Almost periodic differential equations
• The one-dimensional Schrödinger equation with a quasiperiodic potential
• Minimal functions with unbounded integral
• Anderson localization for one-dimensional difference Schrödinger operator with quasiperiodic potential
• On a Floquet theory for almost-periodic, two-dimensional linear systems
• Almost periodic Schrödinger operators. III: The absolutely continuous spectrum in one dimension
• Prime flows in topological dynamics
• Absolutely continuous spectra of quasiperiodic Schrödinger operators
• Generic properties of the rotation number of one-parameter diffeomorphisms of the circle
• Lifting properties in skew-product flows with applications to differential equations
• THE STRUCTURE OF EIGENFUNCTIONS OF ONE-DIMENSIONAL UNORDERED STRUCTURES
• The Structure of Distal Flows
• Almost Periodic Properties of Bounded Solutions of Linear Differential Equations with Almost Periodic Coefficients