Dynamics of a family of piecewise-linear area-preserving plane maps III. Cantor set spectra

DOI10.1080/10236190500273184zbMath1082.37046arXivmath/0505103OpenAlexW2079561663MaRDI QIDQ3369569

Jeffrey C. Lagarias, Eric M. Rains

Publication date: 2 February 2006

Published in: Journal of Difference Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0505103

zbMATH Keywords

Numerical simulationsrotation numbersymbolic dynamicsCantor setsbounded solutioncircle mapsdiscrete Schrödinger operatorrotation intervalarea-preserving maptight binding modelpiecewise-linear homeomorphisms

Mathematics Subject Classification ID

Dynamical systems involving maps of the circle (37E10) Iteration theory, iterative and composite equations (39B12) Difference operators (39A70) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Symbolic dynamics (37B10) Quasicrystals and aperiodic tilings in discrete geometry (52C23) Rotation numbers and vectors (37E45)

Related Items (5)

On the Existence of Chaos in a Discontinuous Area-Preserving Map Arising in Financial Markets ⋮ Dynamics of a family of piecewise-linear area-preserving plane maps II. Invariant circles ⋮ Border-Collision Bifurcations in $\mathbb{R}^N$ ⋮ Critical curves of a piecewise linear map ⋮ Arithmetic exponents in piecewise-affine planar maps

Cites Work

• Localization for a class of one dimensional quasi-periodic Schrödinger operators
• Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations. (On smooth conjugacy of diffeomorphisms of the circle with rotations)
• Cantor spectrum for the almost Mathieu operator
• Metal-insulator transition for the almost Mathieu operator
• The Ten Martini problem
• JACOBI MATRICES WITH RANDOM POTENTIALS TAKING FINITELY MANY VALUES
• Dynamics of a family of piecewise-linear area-preserving plane maps II. Invariant circles
• Dynamics of a family of piecewise-linear area-preserving plane maps I. Rational rotation numbers
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