Dynamics of a family of piecewise-linear area-preserving plane maps I. Rational rotation numbers

DOI10.1080/10236190500273069zbMath1082.37044arXivmath/0301294OpenAlexW2114901255MaRDI QIDQ5717581

Jeffrey C. Lagarias, Eric M. Rains

Publication date: 10 January 2006

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

Full work available at URL: https://arxiv.org/abs/math/0301294

zbMATH Keywords

symbolic dynamicscircle mapsperiodic mapdynamics on rays

Mathematics Subject Classification ID

Dynamical systems involving maps of the circle (37E10) Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) (37N20) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Symbolic dynamics (37B10) Combinatorial dynamics (types of periodic orbits) (37E15) Rotation numbers and vectors (37E45)

Related Items (10)

Center Bifurcation in the Lozi Map ⋮ Conewise Linear Periodic Maps of the Plane with Integer Coefficients ⋮ On the Existence of Chaos in a Discontinuous Area-Preserving Map Arising in Financial Markets ⋮ Bifurcation patterns in homogeneous area-preserving piecewise-linear maps ⋮ Asymptotic Poincaré maps along the edges of polytopes ⋮ 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 III. Cantor set spectra ⋮ Border-Collision Bifurcations in $\mathbb{R}^N$ ⋮ Critical curves of a piecewise linear map ⋮ Arithmetic exponents in piecewise-affine planar maps

Cites Work

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• Ergodic properties of the Lozi mappings
• Absence of localization in a class of Schrödinger operators with quasiperiodic potential
• 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
• Periodic orbits of difference equations

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