Absolute continuity of the rotation number for quasi-periodic co-cycles in \(\mathrm{SL}(2,\mathbb R)\)

DOI10.1007/s11040-014-9147-4zbMath1345.37041OpenAlexW97637519MaRDI QIDQ471823

Sana Hadj Amor

Publication date: 17 November 2014

Published in: Mathematical Physics, Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11040-014-9147-4

zbMATH Keywords

rotation numberabsolutely continuous functionK.A.M. theory

Mathematics Subject Classification ID

Linear ordinary differential equations and systems (34A30) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Perturbations in context of PDEs (35B20) Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations (37A20) Rotation numbers and vectors (37E45)

Related Items (1)

Ballistic motion in one-dimensional quasi-periodic discrete Schrödinger equation

Cites Work

• The rotation number for finite difference operators and its properties
• Hölder continuity of the rotation number for quasi-periodic co-cycles in \({SL(2, \mathbb R)}\)
• 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
• Fine properties of the integrated density of states and a quantitative separation property of the Dirichlet eigenvalues
• Floquet solutions for the 1-dimensional quasi-periodic Schrödinger equation
• A relation between a.c. spectrum of ergodic Jacobi matrices and the spectra of periodic approximants
• Hölder regularity of integrated density of states for the almost Mathieu operator in a perturbative regime
• Regularity of the rotation number for the one-dimensional time-continuous Schrödinger equation
• Metal-insulator transition for the almost Mathieu operator
• Absolute continuity of the integrated density of states for the almost Mathieu operator with non-critical coupling
• Hölder continuity of the integrated density of states for quasi-periodic Schrödinger equations and averages of shifts of subharmonic functions

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