Harper equation, the dissipative standard map and strange nonchaotic attractors: Relationship between an eigenvalue problem and iterated maps

DOI10.1016/S0167-2789(97)00160-7zbMath0925.58057OpenAlexW2132490709MaRDI QIDQ1373353

Indubala I. Satija, Jukka A. Ketoja

Publication date: 18 November 1997

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0167-2789(97)00160-7

zbMATH Keywords

strong coupling limithomoclinic pointssimple transformationcritical invariant torisupercritical Harper equationuniversal characteristics

Mathematics Subject Classification ID

Additive difference equations (39A10) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45)

Related Items (17)

``Critical phonons of the supercritical Frenkel-Kontorova model: renormalization bifurcation diagrams ⋮ NOTE ON STRANGE NONFRACTAL ATTRACTORS ⋮ Renormalization analysis of correlation properties in a quasiperiodically forced two-level system ⋮ APERIODIC NONCHAOTIC ATTRACTORS, STRANGE AND OTHERWISE ⋮ Strange nonchaotic attractors with Wada basins ⋮ Strange nonchaotic attractors in Harper maps ⋮ OLD AND NEW RESULTS ON STRANGE NONCHAOTIC ATTRACTORS ⋮ CRITICAL STRANGE NONCHAOTIC DYNAMICS IN THE FIBONACCI MAP ⋮ Golden mean renormalization for the Harper equation: The strong coupling fixed point ⋮ Golden mean renormalization for a generalized Harper equation: The Ketoja–Satija orchid ⋮ MODE-LOCKING IN QUASIPERIODICALLY FORCED SYSTEMS WITH VERY SMALL DRIVING FREQUENCY ⋮ Renormalization of fluctuations for a generalized Harper equation for periodic continued fractions ⋮ Applicability of 0-1 test for strange nonchaotic attractors ⋮ Birth of strange nonchaotic attractors through formation and merging of bubbles in a quasiperiodically forced Chua's oscillator ⋮ Strange Nonchaotic Attractors From a Family of Quasiperiodically Forced Piecewise Linear Maps ⋮ Phase diagrams of the Harper map and the Golden Staircase ⋮ Self-similar correlations in a barrier billiard

Cites Work

• Strange attractors that are not chaotic
• Quasiperiodically forced dynamical systems with strange nonchaotic attractors
• Products of random matrices in statistical physics
• ``Critical phonons of the supercritical Frenkel-Kontorova model: renormalization bifurcation diagrams
• Existence, nonexistence and universal breakdown of dissipative golden invariant tori. III. Invariant circles for mappings of the annulus
• Renormalization of correlations and spectra of a strange non-chaotic attractor
• The classical Schrödinger equation
• Universal criterion for the breakup of invariant tori in dissipative systems
• Single Band Motion of Conduction Electrons in a Uniform Magnetic Field
• Unnamed Item

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